Over the course of her career, Kathleen Hanna has perfected two modes of performance. The one she uses on stage as a rock star, in which she gives the audience as good as she gets. And the one this approach is in some ways correcting: the shut-down, disembodied version of Hanna that she used on stage many years ago, while making ends meet as a stripper. "So there's this weird dichotomy of complete silence and complete speech," she says. "That's what made our shows so confrontational. I was really pissed off. And I thought, this is my chance to say everything I have to say."

Hanna has a lot to say, and much of it used to annoy people – specifically, rowdy men in the audience at concerts, who would come to rile her and occasionally throw missiles. This was in the 1990s, when Hanna was lead singer of Bikini Kill, the band that pioneered the riot grrrl feminist punk movement with its furious, crashing anthems to girlhood, and Hanna still has vestiges of the punk style going. Today, she is propped up on huge shoes, with big hair and eye makeup, and a tone of appealingly flippant belligerence. After the band split in 1997, she disappeared from the scene for a few years, but she is back touring now, in a band called the Julie Ruin, a 45-year-old with a lot of fans the same age – "professors of women's studies and whatever" – who get weepy at the memory of how much she meant to them during more vulnerable years. "There hasn't been any fighting," she says of her most recent tour, and looks amazed.

We are in a restaurant in lower Manhattan around the corner from where she lives with her husband, Adam Horovitz of the Beastie Boys, and a long way from where she started out. Hanna's early years were often dismal and chaotic, disrupted by moving – the family never stayed longer than a few years in any one place – mostly around Maryland, until they returned to Portland, Oregon, just before Hanna started high school. "An excellent time to move," she says drily. During those difficult years, she would have loved to have discovered something like her own band, she says – someone who told her, it isn't you, it's them – and although the 90s are enjoying a resurgence at the moment, it isn't a message that dates. Over the last 20 years, Bikini Kill records have carried on selling. "I mean, not making a lot of money, but they steadily sell… There are certain Bikini Kill records that have become part of the lexicon of high-school girls who are, like, weirdos. Their sisters give it to them and their friends give it to them. That's been really great."

During live performances, one of Hanna's signature moves used to be to ask the girls in the crowd to come to the front, and her career has, in some ways, been one long campaign to make more space for herself and other women in the room. This was a rejection both of cultural and personal conditioning. For a long time, Hanna says, she was good at making herself invisible as a response to threats from the outside.

She tells an odd story of how, during her early days touring, she bought a gun to protect herself, then ran out of cash and ended up having to sell it to a guy in a car park. She knew how to shoot from being taken to an outdoor range as a teenager by her dad. "I wasn't very good. And it was kind of a sketchy range in LA, where people had M-16s." The place was badly run and people were shooting and hitting rocks, with splinters flying. "And I was like, this is really bad." But since it was her dad who took her there, she assumed it was OK and normal.

When Hanna's family arrived on the west coast, she studied the groups at school and copied, down to the last hair pin, the most popular girls' style. Looking back, she calls it a "social experiment", although at the time it was more like survival. "Kids can be really mean, and when you move in the middle of sixth grade, you'd better get ready to take some shit." She began wearing "Ralph Lauren sweaters and these certain kinds of bangles and made friends who were like that. And I remember hating them and thinking they were ridiculous, but I just wanted to prove that I could do it."

If she was conformist at school, Hanna was starting to find her own style more at home. She began writing poetry, which would turn into spoken-word performances and, after she began singing, at college, be repurposed into lyrics. And she had begun to think vaguely politically.

Hanna's mother would never have described herself as a feminist. But when they still lived on the east coast, she once dragged her daughter to a rally in Washington DC where Gloria Steinem made a speech. And then there was the business of the church basement. Every Sunday, Hanna's mother would disappear for a few hours. "I finally asked her about it, and she said, 'I'm going to a church basement, answering calls from women in trouble.' Later I put it together that it was a domestic violence shelter that they were running through the church. And my mum's not religious at all. I have no clue how she found it."

It was in many respects a conventional family. "A typical middle-class American upbringing" – her father was a sprinkler fitter, her mother a psychiatric nurse. "It wasn't that I lived in this radical household. My mom was very secretive on the feminism." Hanna remembers her mother returning from a trip to the movies one day, ignited by what she had seen. It was the John Waters film Polyester, a satire of suburban life in which a woman deals with the fact that her husband is unfaithful and her children are screaming disappointments. "I remember her coming back and telling me – not my dad, but telling me as a six-year-old – 'My life has changed. Everything's different now. I saw this movie by this man, John Waters, and now I know that I am funny, that somebody else in the world is like me.' She had the same kind of sense of humour as him. She always looked at me like, 'Can you believe I'm a mom?!'"

Bikini Kill would derive a lot of their power from standing up to male aggression, sometimes quite literally, and Hanna would on occasion wade into the audience and physically remove hecklers. In her teenage years, however, she was more inclined to blend in and, even after drifting away from the popular girls, keep in with everyone. "I sold weed in high school, so I sort of had to be friends with everybody, even though I pretty much dressed like a weirdo."

How did that start? "My weed dealer got expelled and I took over his business." She modelled it on the lessons learned from a junior achievement course, designed to teach schoolchildren business skills. "We sold cheese boards, and I made the most money. I realised the best time to sell was on a Friday, when everybody got their cheques, and we were these cute kids selling cheese boards, so we sold loads. And it was only a minute step to selling weed. It always amused me that I learned to deal drugs from a school programme."

Hanna's dealing was never exposed, but she was suspended three times for her own drug and alcohol consumption. Each time, she told her parents she was only marginally to blame – that she was being led astray by someone else – and they believed her. They had bigger problems. "I grew up in a really dysfunctional household where I learned how to go under the radar and check out a little bit. I had to turn my intuition off in order to live in that environment, because you can't live in constant fear. You just shut off."

Fear of what?

"My father. He had a lot of guns in the house and was an alcoholic, and you put the two together and it's not that good a situation." Her parents divorced when Hanna was in her mid-teens, but until then, she says, "I'd go to sleep every night and my dad would get drunk and walk around with guns. I always thought he could shoot us in the middle of the night." (In her head, she thought of her father satirically as "voted most likely to shoot us in the middle of the night".) "My mum's like, wow, I never knew you thought that way. She wasn't afraid of him because she knew him better than I did. But when I prayed and said, 'Now I lay me down to sleep', I meant business."

After Hanna was suspended the last time for drinking and drug-taking, she was made to have counselling. "I had to go to this drug class and the guy running it ended up hitting on me. I went back to the school when I was in college and filed a formal complaint against him."

There is a direct correlation, Hanna says, between the way she felt suppressed during those years at home and the way she behaved, years later, on the road. After leaving school, she went to college in Olympia, Washington state, and studied photography, inspired by Cindy Sherman, and was convinced she would become an artist of some kind. She started doing a few spoken-word performances about sexism and violence against women, then one day ran into one of her heroes, the writer Kathy Acker, who told Hanna that if she wanted to reach an audience, she should get out of the poetry racket and form a band.

The first two groups she formed, Amy Carter and Viva Knievel, were disbanded after a few months. Then Hanna met another hero, Tobi Vail, who had set up the feminist zine Jigsaw and would become Bikini Kill's drummer. They started to make an impact on the Washington state music scene.

They had no money, something Hanna was used to. While still 18 and studying at college, she had considered her options. One summer, she went back to Portland and got a job as a stripper. This was not, she points out, a social experiment. She wasn't hoping to get a memoir or a publishing deal out of it, and these weren't high-end joints. "It was a crappy job. I feel really offended when people act like it was some sort of feminist statement. I don't feel that way at all. There's a frankenstein monster that came out of the riot grrrl scene, which has always bothered me, which is that sex work is a) eroticised, b) exoticised. 'I'm going to write my masters thesis on sex work.' I didn't do it because I thought it was funny.

"Although I'm talking about it now, I didn't do it for the story. I want people to know it's a shitty job, it's degrading and there are women there who were twice my age, paying for their kids' tuition so that their daughters could go to gymnastics class. So fuck you, coming in and doing it for five minutes so you can write about it. It's classist, I guess. Making fun of women who really have to do that job. Wearing a disguise."

In that era, she says, women with tattoos wouldn't be hired as strippers, so she got some tattoos in the hope she would force herself out of the market. Sure enough, when Bikini Kill were touring and the van broke down and they needed $1,500 to fix it, she walked into a strip joint and they took one look at her tattoo and said, no way. Hanna was desperate, however, and asked them to give her a chance, which they did.

What was the tattoo? "Oh, it was roses. It wasn't as if it said, Fuck You. Or Sexism Sucks."

Or, I'm Not Internalising Your Gaze. She starts giggling. "Yeah. Or, Stop Objectifying Me."

It was degrading, but she could do it because she knew how to be mentally absent in a situation. "Having that family history really helped me as a dancer, because I thought, Oh my God, I'm really good at this. I didn't really care what the men said to me; I didn't take it in."

After the van was fixed, Bikini Kill went on tour to England, and the riot grrrl movement started to take off. When they returned, they collaborated on a new single, Rebel Girl, with Joan Jett, and started work on a new album. The band was getting a reputation that provoked both huge support and significant backlash. In England, they had played a women's-only concert, which sold out very quickly and caused a big stir, and Hanna continued to ask girls to come to the front. "I thought, what's the big deal? Men meet all the time. They have soccer teams. Strip bars. And yet it was a big controversy."

She would talk on stage about rape and always be shocked, afterwards, when girls came up to her and said they identified personally with what she was saying. "They'd say, 'I have to tell you something – I was raped in high school.' I was blown away by how saying it on stage – 'Hey, I'm sick of sexual harassment and I wrote this song about being harassed on the street' – would result in women coming up to me every night and saying that. That's what kept me going when dudes would yell, 'Shut up shut up shut up.'"

The heckling became more pronounced once it was established that Hanna could be guaranteed to react furiously. She realises now that the mistake they made was in charging so little for the concerts. Tickets at that time were around $5. "It's not very much to spend, five dollars, to come and yell at someone. Guys would come to yell really horrible stuff, call me all kinds of names, sometimes be physically violent. And later, when we charged $12 a show, it didn't happen. Because no one's going to pay $12 to harass this women's band. But it became this thing, like, oh she kicks guys out. We played clubs that didn't have any security. People could get away with a lot of shit, and if I wanted to get someone out, I had to physically do it myself. I remember playing in Oklahoma and this guy was messing with me and I said, 'That's enough, get the fuck out of here. For $5? Go and get your money back.'"

There was a backlash among some women, too, from feminists who called Bikini Kill and the riot grrrl movement too white and too middle class, which Hanna has sympathy with. Male journalists would try to get a rise out of her, too. "Like in fanzine interviews, the guys would ask me really rude questions – 'So you're a reverse sexist and you hate men, can you explain that?' And I'd be like, fuck you. But then it became this thing of, 'Kathleen said fuck you to me.'"

Why carry on in the face of such opposition? "I just wanted to make sure other girls found out about feminism. It didn't have to be our mums' feminism; we needed to build on what they had created and change it and make it better, the way this generation needs to do that."

And she was propelled by wounds from her childhood. "I thought that it was all my fault, that my disgusting body somehow drew all this negativity towards it. And having grown up with that feeling, I wanted to make sure that other girls get to this [understanding it's not their fault]." Bikini Kill were never stadium rockers, although they had a big impact, and Hanna never judged the band's success on sales or audience size. "It was when girls came to the front by themselves and were singing the lyrics. The way that they sang them was, 'This belongs to me.' And I wrote them because I needed a community. I was as alone as those girls were."

After the band split up, she carried on solo for a while and then, as she revealed in The Punk Singer, a documentary film released in the UK later this month, she was diagnosed with Lyme disease and unable to work for a long time. Coming back now, with the Julie Ruin, is a different experience, at a different time and age, and with multi-generational fans; middle-aged women nostalgic for their youth, and young girls finding a voice through their music taste for the first time. It falls in the context of a contemporary music scene Hanna admires. She likes Pussy Riot, successors in some ways to Bikini Kill. "I love the Screaming Females. The Younger Lovers is a band I really like. Brontez Purnell is a riot grrrl, a total Renaissance man."

There were more male fans of Bikini Kill than they realised at the time, she says. "A lot of men and boys were influenced by riot grrrl, and I think that's something people don't get. A lot of gay guys, and also straight guys who were standing in the back because they thought that was the thing to do." It was the thing to do, although during the onslaught it would have been good, she says, to have known "that I had backup". Anyway, times change. "I don't say 'girls to the front' any more," says Hanna, "because they're already there."

• The Punk Singer is released in cinemas on 23 May.