>>14
Sure. Ask for her contact info (email or AIM) so you can keep in touch. If you get some info, say, "Hey, maybe we can find some time later to hang out and grab a bite to eat."
The key to this is that you hint something down the line, making you seem less desperate, which in-turn leads to a more comfortable environment.

E-mail her a couple days later and go from there. Ask her what her final grade was in the class, how she liked the class, ect ect. Just find some really easy convo. points so you both can get accustomed to talking to each other. If there are a few messages sent back and forth, move on to meeting up in person.

One key piece of advice- do not talk about everything you can think of in the emails. Keep them shout and sweet so you can have some stuff to talk about when you meet.