I understand your fear of rejection. It’s very common. You’re afraid of things not working out and losing contact with her. But I can tell you what’s worse than rejection: regret. If you lose her because you never get a shot, and she was the one, you’ll feel a lot worse than you do because you’re afraid of rejection or things not working out. Let that be your motivation.
Get out of the friend zone and be the guy. Your’e the one who’s responsible for asking her out, making the first moves and leading. She may be anxious because she sees your reticence to invite her out on a date or initiate sex. This may make her think you’re just going along and are not that into her, in spite of your having a great time. From her point of view, you’re not taking the lead — and that’s probably from your point of view, as well. Your taking the lead is what will send her the message that you’re in. Be careful to behave in a way that reflects your intention.
Hope that helps! 🙂