Been there, done that. Meeting women in college was very hard for me. I would get nervous, self concious and basically terrified. Bleive me, I know where you are coming from. I can offer some advice, but its not easy advice to follow
1) Be willing to take a chance - I don't care how scared you are, you will never meet her if you don't talk to her. This means starting a conversation in spite of the fact that you are nervous. Its hard, but the only way through it is to do it.
2) Expect success - Approach the whole situation as something good that is about to happen in your life. This is tough, becuase your nervousness is telling you to expect failure. In fact, they only way to truly understand this is to succeed a few times, and the only way to succeed is to keep trying. I guarantee there are women out there who really want to get to know your. Sounds like this lady might be one of them.
3) Listen to her - I cant stress this enough. Don't try pick up lines or other nonsense. Just start talking to her about anything you have in common (such as the class you are both in). If she is interested, she will eventually share something small about herself or her interests. LISTEN for it and make sure you give her feedback. Women appreciate men who listen to them. Its one of the most romantic things you can do.
4) Don't dwell on failure. I asked out many women before I met my wife. Many said no. It was depressing at times, but I refused to dwell on the failures. In the end, the woman that mattered said yes.
5) {I almost hate to say it) Be yourself - Yes, that old chestnut again. This is another one of those bits of advice that is hard to understand until you've succeeded at it. Until you can relax, you are putting on an act with women and they can spot it a mile away. I know its hard, but try to forget that you have a romantic interest and talk to her like a good friend whom you are at ease with. Again, thats much easier said than done, but if you keep this goal in your mind, you willl eventually figure it out.
I wish you all the best my friend.