She certainly seems interested in spending time with you.
Why not ask her for a soda or something after class and see what happens? If it's nice and you have fun, say something like, "I had a really good time. Let's make the next time a real date. Say, this Saturday night?" And see what happens.
I am suggesting the soda and ambiguous date/nondate to start, as it gives everyone plausible deniability. E. g. if you have a lousy time or she doesn't seem interested, then it was a soda and it was friendly and everything's cool. You haven't mangled the friendship.