Saying "just ask her out" to someone who has not tried that approach is probably good advice, and has worked for a lot of people, which is why so many are quick to suggest it. For me, however, if the first date doesn't come about organically, it's probably not going to work.
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.
Ok, here's why being simple about things doesn't work for me. There is a social template for dating, a way that people are expected to act. Part of this is that people are typically on their best behavior. If I'm dating someone and they stick to the social template, it prevents me from getting to know who they really are. It also causes them to appear to be dishonest and that kills any attraction I have for them.
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!