I've noticed one of my classmates in college seems to have noticed me more than she's noticed most others. She tends to say 'hi' and try to start conversations with me when we're waiting for class to start, responds more to me than she does to most others, and more than most others respond to me when us and our other classmates talk outside the classroom waiting for class to start, and her reactions are generally agreeing with me and trying to continue a conversation. After our first 'real' conversation, she added me to facebook later that day (and she hardly has added anyone else from the class, so she's not just one of those people who adds everyone). She however hasn't (to my knowledge) tried to flirt with me or anything.
I really can't tell if she sees me in any romantic sense, is just being polite, or is just another introvert who feels more comfortable around me. Anything specific I should look out for, or do to find out? I see a lot of potential here, but also don't want to make things awkward if she doesn't have any feelings for me. I'm thinking of asking if she wants to hang out during lunch break or something, does anyone think this could work, or have any better ideas?