Not that I think it is necessarily *wrong* for a girl to do the asking, but I tend to be pretty traditional, and so I consider that to be the guy's job. Besides, I wouldn't want to be stuck with a guy who lacks the balls to ask for what he wants.
Your job is to make yourself very approachable so he feels comfortable asking you out (if that was what you want). You will have to get a hold of yourself and your shyness. Next time you see him, smile and say hello. Ask him if he enjoys this class, blah blah blah.
Relax... I'll need some information first. Just the basic facts - can you show me where it hurts?