I would agree that patience is the trick--
Also, looking at it from a girl's point of view--what if she's actually as shy as you are and what she sees is that you're serious and say hi to her but that's all? she might be wondering what you're feeling but she might not make a move either--
Like others have said, just be yourself, and also try to approach her and talk to her--regardless of any feelings of love you might have, you want to be her friend, right? so, how would you approach ANY OTHER potential friend?
good luck!
tantrika-