How/Should I bother asking her out?

Okay so I'm currently taking drivers ed' cles in California. Now there's only two days left of courses and there's this girl in there i really like. I think she knows i like her also. Let me try to explain on the first day of cles I didn't really think much of anyone in particular in there i was more focused on the drivers education cl itself, and eventually I saw this girl(she is gorgeous), and i just couldn't help but glace at her on occasion. Then i noticed she glaces at me alot also. Now I'm not trying to sound coincided, but I know(and have been told) I'm very attractive. So there's only two days of courses left, and she is always talking with her friends, or looking over at me in some way, shape, or form. How do I ask her out?(I don't even know her name). Not to mention I'm a slightly shy person by nature. I don't want to come off as strange by the way I'm just looking for some suggestions, and I don't necessarily fear rejection, but a few girls have asked me out in the past and I have rejected them(but asked if we could still be friends of course). Any Suggestions peoples?