Darklance, I have to agree with takyris- get to know this girl first, then ask her out. Right now you are going off a feeling, without even knowing much about this girl. It might be you guys don't have anything in common and wouldn't be happy together, or you guys might be perfect and have great times. But I'll guarantee you that going up to a woman and asking her out when you haven't said hardly anything to her is likely to spook her and make it more likely she will avoid you.
I'd try to make friends with her first. Heck, she'd probably be impressed that a guy wanted to be her friend BEFORE he starts expressing romantic overtures to her. If she is really pretty as well, she probably isn't used to being treated like this, and will be really impressed.
The other thing is to watch her body posture and reactions to you when you talk. If she makes lots of eye contact, laughs a lot, smiles often, and plays with her hair, its a good sign she likes you. If not, she might warm up to you once she knows you better.
From experience, the best thing you can do is just try to be a nice guy. Don't try to brag and be boastful, instead ask how she is doing, what she has been up to, and ask questions about her. Some girls like the braggart jock types, and if she is one, she probably isn't right for you. Over the years I have met lots of women, and I have a ton of very close female friends. Even if she isn't interested in a potential romantic relationship, you should be able to make a friend. And believe me, when you behave this way and meet a girl who is comaptible with you, you can brag to all your buddies about how you have the coolest, most gorgeous girlfriend (and thats something most girs don't mind you bragging about).