I agree with Warped. But anyway, I suggest you do this:
1) Practice - the more you approach, the easier it will become, you will learn the feeling that nothing bad happened - and at least in my experience lot of good things happened when I started approaching more
2) It sounds from your post like you are insecure about yourself. On the one hand you elevate this girl you haven't even talked to to some sort of dream girl and at the same time you consider yourself not very good looking.
The fix is to go and think what it is that you think is not good about you, and work to improve it. Are you not good looking because you are fat? Go to gym, follow exercise plan, and eat reasonably well. Bad clothes? Look at some fashion pics online and try to buy some clothes that fit you and go well together. No clue about that? There is lot of stuff online.
You get the idea. When you fix the problems, then you will not feel like there is hundred kilometers between you in terms of looking good, being good and so on.
Oh and when you talk to her, just say what you feel, i.e. you saw her, think she's cute or something, so you had to talk to her, whatever. Don't think for half an hour in order to come up with "oh I see you are looking at spring onions... Are they in season now?".