I think you are complaining too much about your past relationships, and of your doubts and fears. All those issues are for you to deal with, not her. She could read it like this "A nasty girl hurt me in the past, and I hope you won't be a bitch with me". You sound insecure, vindicative, and put her under pressure, instead of taking responsibility for your past choices and experiences.

You should sound much more confident and optimistic,... You have decided to write the letter, and that is something positive. Keep your doubts for yourself, don't force them on her.

So I would suggest something like this:

"Once I lost faith in love, and have since lived as a free man, untroubled by such emotions. And yet your charm has broken the slumber of my heart, and it burns with a wild fire. Your elegance, wit and beauty have smitten me and rescued me from the pits of cynicism.

You were always precious to me as a friend and I don’t really remember when I started to see you as something more than a friend. All I know now is that a week without seeing you feels like an eternity to me, and the thought of you leaving me tears me up inside. Though it takes a bit of courage to start a relationship and open one's heart, I believe that one must take chances when presented with an opportunity for something wonderful to happen. So by your permission I would like the chance to get to know you better, take you out on a date, take a step further than friendship and see where fate leads us."

Good luck!