Listen to Vector. You can't force a relationship. If she doesn't want it, don't press the issue. If a good friendship develops, it's only grow by letting it happen naturally.
My best advice is more about life in general: Be yourself, and don't try to force yourself to be something else. Life is about becoming, growing and developing, so you might as well relax and steer yourself towards it slowly. You're not going to change over night, and you're not going to do yourself any good by trying.
She may be uncomfortable around you because you're so desperate to be someone else around her. You want her to see you in the same idealistic way she sees you, but you think about it too much and try to force yourself to be something that you're not - And, what's worse, you don't even know what you're trying to force yourself to be, because you don't know what her ideal is. Whatever it is, though, your subconscious is absolutely convinced that what you are is not it, so you try to be something else. She's picked up on your confused attempts to impress her, and she doesn't like it, because it feels like you're trying to force the relationship, too.
Think about it for a second: Can you really blame her? How would you feel if a girl tried the same thing with you? You'd much prefer that she just be herself so you could get to know her, right?
Despite how a lot of guys think, women aren't mysterious or omnipotent in any way. (Just don't tell them that. They work really hard to keep that ruse going.) They aren't objects or puzzles to be figured out, either. They have a slightly different way of looking at things, but in the end they're human, too. Like most people, she'd rather have a serious relationship based on trust and understanding. Since it's hard to trust and understand someone that acts differently around you, she's probably just avoiding what could definitely be a bad relationship. Be grateful for it: This is probably saving you and her a lot of heartache.
Focus on just being yourself. If it turns out that her ideal isn't what you are, then I can guarantee one thing: You two never would have been happy together.
If it does turn out that you're compatible, best to let things go naturally - Since she was the one feeling uncomfortable, let her be the initiator. If you try forcing the issue again after becoming friends, you may lose all the ground you've lost. So let her make the first move towards something more than "friend".