Whatever you do, don't compliment her excessively, try and play hard to get. And there's a good chance she may not like you to begin with- if that's the case you're kind of screwed. :P
Y'all suck. I'm gonna flat out tell you that she may know your name, but so does every other person in your class. Also It's high-school, it doesn't matter at all. I estimate a .01% chance of her saying yes if she's not even your friend or someone you know.