The problem with writing a letter is that you can't take back what is written down. Also when she reads it, she may interpret it her own way anyway which maybe confusing as well. I think the best thing you can do is just not say anything at all. This year you guys have had was a healing period for the both of you, and there is no sense and rehashing old bullshit. If she's happy with her new guy, just leave her be. I think that part of you hopes there is a way to make things right again, and you even said it yourself that you still have feelings for her. You do have an ulterior motive. Leaving her be is the best thing you can do and if you are truly sorry for everything that you have done, the knowledge itself should be enough to make you feel better. She'll forgive you eventually, don't worry about her hating you forever and ever. Only she knows when that is, and if she isn't ready to, nothing you can say to her can change it anyway.
Waking up next to a beautiful girl,
Step outside and say hello to my beautiful world.