Jaja, ok first just be relaxed and keep it cool. You don't have to worry and think you can be needy, just play it fun and invite her with some of the following (depending on what do you want to do):
-Hey, I was going to check out x movie, but I need an expert in this topic. So if you are, why don't you join me and I'll test you?
-I'll get a cup of coffee (or ice cream I prefer) after class. Why don't you come over?
-(The most basic one haha) Care to join me in (say place) at (say time)?
Just invite as you would invite a friend, only with the C&F attitude, and just don't worry. Don't show a lot of interest and don't think it, and you won't be seen as needy or wuss.
And another councel: DON'T ASK her if she wants to go with you, INVITE HER to join you, as if you either didn't care if she wants or not.
Hope it helps, good luck buddy