Honestly, it sounds like he has more issues than just bipolar. Don't take it to heart.

Your ex bf sounds like he has trust issues. This was an old letter, part of your past, not future. It sounds like he took this and blew it up 100 fold. He sounds insecure, and yet he is telling you that you are. There probably isn't anything more you can do. But why grovel and beg, when you didn't do something wrong in the first place.. Regarding the letter. If you have done nothing wrong you have nothing to prove.

I'm sorry that you are going through this, I know it hurts. And that's not easy to deal with. Focus on yourself here too, take care of yourself. Take some time and reflect on if this is really what you want.