Take things one step at a time and don't go the the next step until you've received a positive response regarding the step you're on. 1- smile - that's it - just smile at her - a nice easy smile; 2- smile and raise you hand up about half way to your shoulder in a hi sign when you first see her; 3- smile, raise you hand and say Hi. (Now since you haven't exploded or dropped dead, at least not yet, you should have gained a little confidence - plus she has responded positively to each step you've taken. Soooo 4- Smile, raise your hand, say Hi - then all of a sudden like you just thought of it take enough steps toward her so you can say something and say, "Hey, my name is George. What's yours?" bla bla "Great. Glad to meet you Suzie, now at least I have a name to put with the Hi." smile and walk away; 5- Smile, raise your hand, say Hi, Suzie - and when you're ready (another I just thought of something) "Hey, Suzie, why don't we hang out sometime? I'd really like to get to know your better."
If you will take each of thsoe steps when you are comfortable AND have received positive feedback from her, you will have made significant steps toward getting over the shyness. Good luck.