A girl in class

So there is a very good looking girl I sit by in class, shes a freshman I'm a senior (no I just dont want something physical) I like her. However, shes really shy. We do talk in class and I make her laugh and what not and we talk about stuff but thats about it. We also chat on Twitter and stuff. I know shes single because she's told me and we are into the same type of things but how do I go about taking it further and showing her I'm really interested?

Simple ask her out to a movie or something. That's how it's done. Oh and do it in person, not IM.

Ask her to do something with you. . . even if it's just study.

go a head, ask her to do something together