“What a great space,” someone says as we enter the old Bakhmetevsky bus garage in Moscow. But that scarcely begins to do justice to this unimaginably vast, parallelogram-shaped chamber, built by the Constructivist architect Konstantin Melnikov in 1927. Here, for decades, Soviet mechanics toiled and sweated – or perhaps shivered from cold or the fear of denunciation and arrest. But like the USSR, the buses and the workers have gone now, and one night in June, an altogether different group of people gathered to toast the garage’s new role – as a private but non-profit gallery for contemporary art.

It is quite a sight, the international art world en masse and working the room in a kind of slow Brownian motion. There’s a lot to work, given both the dimensions of the room and the fact that this is such a target-rich environment for anyone keen on schmoozing. Some major collectors are here, including cosmetics heir Ronald Lauder, hedge-fund boss Steven A. Cohen and Ukrainian oligarch-turned-philanthropist, Victor Pinchuk. There are artists such as Jeff Koons and Rafael Lozano-Hemmer, whose lighting “tree” sculpture is the only artwork in place for the party. Gallerist Larry Gagosian – who opens a commercial gallery in Moscow this month – is here, along with his former lieutenant, Mollie Dent-Brocklehurst, now international director of the Garage. And mingling with them all and grazing on canapés are some seriously rich, chic Russians.

For anyone not wowed by all that artiness, the show has also got even the British tabloids’ attention: Amy Winehouse has reportedly been paid £1 million to perform. Will she appear, we all wonder – and will she be late? Out of it? Brilliant? (There was a bit of a wait, it’s true, and whether she was out of it or not was a moot point, but the performance was certainly brilliant.) The tabloids are also interested because our hostess tonight, Daria (Dasha) Zhukova, the 27-year-old Russian It girl who had the bright idea of turning Melnikov’s garage into Russia’s leading contemporary art institution, also happens to be the girlfriend of Roman Abramovich: oligarch, former provincial governor, owner of Chelsea FC and now, since he paid top dollar for a Bacon and a Freud earlier this year, emerging as a new major collector of art.

They make a glamorous couple, everyone agrees. Abramovich – looking dashing and actually rather hot in a tux, rather than the humdrum stuff he wears to the footie. And Zhukova, a real beauty, but clearly also a brainy one, as she inaugurates the project with a speech, first in Russian, then in flawless American-accented English. For the truth is that while it might be tempting to present Zhukova as simply a dazzling young trophy – and she certainly looks dazzling – or even a young gold-digger (and people occasionally have), that amusing narrative is pretty wide of the mark.

She’s wealthy in her own right, for a start, though perhaps not in Abramovich’s league – the daughter of Aleksandr Zhukov, who first made his fortune “in oil”, as she puts it when we meet up in London this month (and not, as has been widely reported, his namesake, the long-serving Russian deputy prime minister). Her mother is a professor of microbiology in California, where Zhukova largely grew up after her parents divorced – thus the accent – and studied literature and Slavic studies at the University of California, Santa Barbara.

For many young Russian women Zhukova represents a different kind of icon from a mere trophy beauty, because she’s savvy and professionally ambitious as well as attractive and chic, rather than bling, like an earlier wave of post-Soviet lovelies. And in common with her good friend Polina Deripaska – not just the wife of an oligarch, but also head of the publishing group FMG – Zhukova has always worked. She launched what she describes as a “small but successful” fashion label, Kova & T, with her old schoolfriend Christina Tang, and while by her own admission, she’s not “some art genius”, she has put all her energies and star power into getting the Garage off the ground.

“I think it’s just part of my personality that I’ve had since I was little,” Zhukova says of her work ethic. “And I’m sure my mother and father helped shape that. But I have a feeling I was born with this itch to do things… and of course I want to try to make them successful – ideas and projects and the realisation of things that I think are cool.” She doesn’t especially enjoy shopping (“I can’t shop for long”), rather seeing money as a tool which “can help you to create, to realise ideas”.

I ask her to describe growing up in LA (where the initial difficulty was “not speaking English at all... that was a bit of a challenge, but I quickly adapted – I think I quickly adapt.”). “Give me an age,” she bounces back at me, and I say 14, an interesting age... “14? I was playing volleyball. And organising. My friends and I loved going to Palm Springs, so we’d organise garage sales and sell off our parents’ things so we could go,” she giggles. “I don’t know why we didn’t just ask. If we’d asked them for money they’d probably have given it to us. But it just seemed to be more fun that way.”

More recently Zhukova asked a number of investors, including Abramovich, to put money into the Garage. Abramovich has also sponsored the opening show of works by the Russian contemporary artist Ilya Kabakov. Zhukova wasted no time in forging new relationships in the art world at the highest levels, recently visiting Damien Hirst in his Gloucester studios, agreeing to co-host the planned Serpentine Gallery party last weekend, and assembling a remarkable group of people to advise her, from Dent-Brocklehurst and Gagosian to a broader, at this stage informal group of art world heavyweights, including the Tate’s Sir Nicholas Serota.

As Zhukova sees it, “There is no other institution in Moscow like this and I think a lot of people are excited to have Russia take a step in this direction. So everyone’s been very supportive, simply because they’re fond of the idea.” There are, she explains, contemporary art galleries, but nothing like the internationally recognised, museum-like institution she hopes the Garage will become. “A lot of people feel that Moscow, with its history... [and] as an up-and-coming cosmopolitan city should definitely have a space like this. That’s been a big help.”

She’s also looking for sponsorship – and given Zhukova’s own cachet in Russia, now arguably the luxury goods industry’s leading market, it’s not hard to imagine some fancy-schmancy brands being only too willing to be associated with such a high-profile project. Interestingly, the second show at the Garage will be of contemporary art from the large collection of luxury goods tycoon François Pinault. “A great show for us,” says Zhukova, “given that many Russians aren’t so familiar with a lot of contemporary art, and his collection includes the best of many different kinds of work.”

Zhukova has had no formal training in art, although she has “always been interested in art – and consequently or coincidentally, so have the people around me, which exposed me to many different types of art and artists. My dad is really into architecture and photography, and both of my best friends are artists.” Just how much Abramovich’s new penchant for collecting art is down to Zhukova’s influence has been eagerly debated – although he began sponsoring exhibits at Somerset House organised by the Moscow House of Photography two years ago, before they were dating. “You’d have to ask him,” Zhukova replies when I ask what got Abramovich collecting. (And indeed, try as I might, their relationship remains off limits; after we spoke I e-mailed a “cheeky question, I know,” about whether the couple plan to marry, and got the pithy response: “Cheeky. N/A. xxx.”)

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