You didn't really mention how long you dated this girl, if you dated this girl at all? Just curious about that because you say you treated her like gold but she abruptly stopped talking to you? How old are you guys? It could help me better grasp the situation.
As for this whole situation, I think that maybe she wasn't ready for the level of commitment you were projecting. It seems like you fell hard and fast and all this talk about her being the "one" could have really scared her. Not saying it's your fault as she is clearly not mature enough to communicate and be honest with you about how she felt, but maybe you came on a bit strong from the beginning. And while she may have felt the same way you did at one point, maybe that feeling changed. She was afraid of it seeing as how she already said it and you are holding her to those words. All very possible explanations.
So she's dating the wrong guy and dating a "loser". Guess she will learn that the hard way, eh? It's not like you can just come out and tell her to stop dating the guy because he sucks, she's probably going to want to date him more because of that. If he sucks, they will part ways in due time. And even if they do, it's not guarantee that she will reenter a relationship with you and everything work out to be happily ever after.
While you can't help how you feel, you have to come to terms with it. You loved this girl but no matter how much you love this girl, she just doesn't feel the same way. I know you are trying to read into how she feels through her actions, but no matter what she does, if you guys aren't together or talking about getting together at the end of the day, it doesn't matter. If she wanted to be with you, she would. She knows how you feel and she can assume you feel that way until the day you can tell her "I don't feel that way anymore". And I think the only reason she was jealous you were dating somebody else is because she liked the attention you showered her with, and she was losing that to somebody else.
Which is why the letter is unnecessary. Maybe you think you can tug at her heartstrings with a heartfelt letter or email, maybe you think it will lighten the burden you feel on your back from everything that has happened. It is totally unnecessary man and may actually make things worse. Remember when you projected your feelings for her before and it scared her? What do you think a letter is going to do? It's going to actually make her feel like she could come to you whenever and give her the cushion she needs to find somebody else. Or if she is dating that guy still, it's extremely inappropriate. I don't know how long you guys have been apart but if you haven't been having regular contact with her, how do you know she hasn't changed into somebody that you wouldn't care about? You are basing your feeling on who she was when you got to know her and she could be a very different person now. So your letter could be very inaccurate and you could be just concentrating on the good stuff when she could have some serious flaws you overlook. And if you tell her how awesome she is, you are actually stunting her growth as a person. So if you want my opinion, the letter is a no go.
The best thing you can do is just let it go, let it be and follow a path that you have complete control over. You are responsible for yourself and your happiness, and if you focus on that I promise you will meet somebody that can fit into that lifestyle better. You are probably going to always have feelings for her at least a tiny bit, and that's okay. Like I said, you can't help that. But she is not the only one for you out there. You've already met and dated somebody else and maybe that didn't work out but there are more people out there.
Waking up next to a beautiful girl,
Step outside and say hello to my beautiful world.