But in class, I am a completely different person than I am in real life---in class I am able to hide my real personality and life, and I deliberately avoid making close friends so that I can keep elements of my life secret. For this reason, I think, asking her out may be impossible. After all, what do you do on a first date except ask the other person about themselves? I would be doomed.
I was the same as well. Everyone thought I was pretty normal, maybe just a little shy or quiet. In fact, a lot of the people in my class tried to become friends with me, and for the most part I was treated normally, but thats where it ended; in the class. I know you may be thinking you are completely different, but it doesn't matter. That was one of my excuses, that I was just too different and if she actually spent time with me and found out what I was really like she would be completely disinterested, think I was boring, or whatever. Maybe it would have been true, but I never found it. Maybe she is a completely different person in private also and would actually end up liking your true personality. Or perhaps not, but those things happen. Thats the whole process of dating. Of course, even though I know this I've never actually been on a date because of the avoidance and that is what always holds us back.
You may feel sick and trapped by this whole dilemma. That's how I felt. I really wanted to do something with her but at the same time I always avoided her for fear of all sorts of stupid $#%^ and her finding out what I was really like. But if you don't do something about it you'll only feel worse and worse as time goes on which can lead to more problems as it did with me. I don't know, maybe it won't affect you as much as me and it's not like I can lecture you on this (pot calling the teakettle black...), but seriously, you should do something about it.
Just ######6 go for it! It may prove to be unpleasent, but in the long run it will be well worth the effort. I wish I could make you learn from my mistakes, but you'll have to figure out on your own. I know how hard doing something like this is. Seems like it should be simple since you already know she likes you which is just what I thought. But it just felt like the task was the equivalent of a cripple trying to jump to the sun; utterly impossible. The reality is that we aren't really crippled, and it's only a simple step forward. Even if it ends up being just one date, so be it, life goes on. I think you'll feel better overall in the end.