I think its been said before but girls like a man with confidence.
JUST ASK HER. It sounds like a bad idea and you'll look like an idiot infront of her friends but honestly, if you make yourself believe you're the coolest guy on earth and then just ask her there she and her friends are bound to find you atleast slightly attractive for being so confident.
Also if you do manage to go out with her dont be all "Where do you wanna go...? Is it ok if i do this? Are you having a nice time?" I mean have some control over her. Girls love a man with power and thats one way of showing it off.
You can also be really fun. Thats how i got with my current girlfriend. We met during the day in a gtoup of friends and i kept making her laugh. At the end of the day she was leaning on my shoulder in town so i just put my arm around her. Been togethor ever since. :)
Good luck btw and if you do get with her or even just go and ask her, /brofist.