I used to be this way too a few years back, I had real anxiety approaching any woman that I thought was hot. i'm not a bad looking chap myself, but the problem was rooted in low self-confidence and self-esteem (kept well hidden in day to day life, but there nevertheless). Then I started to think "Screw it, what's the worst that can happen" and just went up, smiled and talked to them... and by that I mean just talked... no cheesy lines, no forced witty banter... just talking normally. For the first dozen times I kind of fell foul of my own nervousness, then as I got more comfortable I gradually realised that very good looking women are not some kind of awe-inspiring, mystical creatures with one foot in another world, they're just normal people who just want a nice conversation the same as anyone else, and if you stay cool and calm during the first half hour and get to the stage where you're both comfortable talking to each-other, the rest is a breeze. Even if they don't fancy you, they appreciate the thought and compliment, and each time you do it gets easier.
Practise your best smile (that's what starts it all off), make direct eye-contact whenever possible when talking to her, and just be yourself. If she likes you then the rest will follow from there. God knows how many men have missed out on a chance to get with their dream girl simply through being too afraid to talk to them, and I know for a fact that many hot women actually get sick of no-one approaching hem, to the point where one of my friends wishes "she was uglier". Most amusing.