Re: how to get over "the approach"??!
Like virus said, just get used to approaching people first. A simple high, my name is ___ is always good. You could also memorize one or two opinion openers as these apply to everyone (instead of trying to come up with a personalized opener for each girl). "Let me get your opinion on something- is it ok for guys to wear makeup?" And go from there. Whichever you choose, then just go for it. You might get blown out of the water at first (it takes some practice to learn the different paths the conversation could go and how to handle each) but it will come naturally very quick.
You are the prize. She needs to earn it.