@ccook4,
Introduce yourself and get to know her! Truth: most very good-looking people (any gender) aren't approached much because so many people are terrified of them.
So be your polite, awesome self and say hi and talk to her. Do this for a few weeks (a month, maybe), and then ask her for a coffee or a soda after class (whichever is appropriate). Have a lovely time, at the end, tell her you did so, and then say, "I had a great time, ___ (fill in her name here). Let's make the next one a real date. Are you free Saturday night?"
And see what happens.