In my early days, my most successful relationships were with girls I knew through theatre. The common interest was already there, you see the best and worst of people through rehearsals, and you gradually draw an eye on someone who might be interesting. Since you've already mentioned music, if there are any social activity groups you're already involved in (and I don't mean solely through online sites, those didn't exist when I was 20), that's an avenue to consider.
Can I just ask about this "other guy", seen as you saw the pics he put on Facebook do you actually know him in real life then? Either way I'd consider simply removing him or even better blocking him on Facebook. I've been there before a while ago where I was jealous of another guy and was almost stalking every activity he did on FB as some clue to him being after my girlfriend. Trust me it doesn't lead to good things, and its annoying "not knowing" but maybe that's better than "assuming." It all sucks, and as others have said whatever she decides then its her decision. I got screwed over by a girl once and was feeling crappy for a while, but some simple words my friend said stuck in my head over and over and made me feel better- "if that's the kind of person she is and that's the kind of things she does, then you're better off without."
Been too busy to post here for awhile. Asking her out after having positive experiences in class is organic! It doesn't get much more natural than that! I suspect that you're just nervous about it. That's natural and you just need to work through that. Whatever approach you use, at some point it usually comes down to that, asking the girl out. Perhaps you'll get lucky and they'll ask you out but that's really just leaving it to luck. That sounds like an excuse to me. But, find what works for you and then find ways to make that happen more often. Right now it just seems like you're not doing much to get things to happen! Mr Awe