From what I can tell you seem like a very sweet guy. I don't have too much room to talk about this topic though, since I'm only 15, but I'll give you my opinion Sorry if I talk about myself too much...
I can completely relate to what you went through in school, since I'm going through it now. I always dread talking out loud in class, or getting called on, I immediately blush and get embarrassed. I'm still not very good at talking to boys.. But the other day this guy commented on my shirt, so I asked for his sn. I knew I would regret it if I didn't.
So I think if you don't ask this girl out, you'll regret it too. Before she leaves, maybe you can privatly ask her if you could email her while she's gone... If you don't want to do that (or even if you do) maybe give her compliments (girls love 'em) and tell her to have a nice trip before she leaves.
I think it sounds like she's at least interested in you. Since you're shy about going out to bars etc., maybe ask her out for a drink in a quiet restaurant or something.
Whatever you do, good luck, and please post again to let us know how it went.