Trust is a very fragile emotion

If she's been betrayed in the past and knows you have been capable of betraying someone then it will be a huge hurdle for her to get over....trust me..I know!!
My b/f has a chequered past in that respect, and whats worse for me is I've been a close friend of his for years before we got together so i know far more than a g/f should!! But I'm sure there are many blokes on here that will put their hands up to being players in their youth but having found the right woman at the right time it has completely changed them! Its called growing up!
But seriously...be very careful with begging her back, you were spot on saying
You don't know what you've got till its gone trouble is....you know what you had because she's the one thats left, but at the moment she doesn't have the same feeling of losing you, she's in control and she knows that if she wants to she can change things at any given time........I know this because I left someone and was in the same situation with him chasing me, sending beautiful letters, flowers, everything imaginable but I found it easy to push him away...until one day he stopped, then I found out he was with someone else....and yep...you guessed...I wanted him!!!
IMO I would send her some flowers or a teddy anything special to you both with simple a letter telling her you Love her, you respect her decision although it hurts so deep this is your last ditch attempt to persuade her that your relationship is worth fighting for, but its because you love her so much you are giving her the space to decide if her love for you is great enough for you both to start afresh and go on to be stronger and happier than ever.
sorry, waffled there....and some may think its not the best idea, but as I said, IMO and in my experience.