Well, a great way to keep in touch with someone you don't see often is to talk to her online, through IM or text message as i'm sure you know. Learn to read her non-verbal signals, and pay attention to what she says and how she responds to you. It sounds like you have a good start there.
I mean, the best way to find out is the direct approach; ask her to hang out or if you're feeling brave, go on a date. Rejection is scary, that's for sure, but it's worth the risk!
You really have nothing to lose by asking her, just be honest! You can do it!