What should I do?

I was dating this girl for just under 3 months. It got very serious, very quick (she moved some stuff into my house, stayed here every night, spoke about marriage/kids, met the parents). It turned out being too much too soon. Trust and temper became an issue on my part (because I felt she was not committed) and it caused her to move out. Since she has said it is over but there are mixed signals. She contacted friends of mine to see how I am doing and told them she needs her time and space. I called her dad and he said that she is hard to change her mind but he suggested I write a letter addressing trust and temper and how they will not be an issue if we were to ever start over. She does not block my emails or texts. She asked to get lunch with friends of mine that she never connected with when we were together. Since our break up I have emailed her and sent texts apologizing and confessing my love to her. Sometimes she responds and says it is over and other times she does not respond at all. The one time I sent an email where I say I am not going to keep trying she calls me but when I ask to get back together, she says no. Some of my friends suggest 1) she will do things on her time not mine, 2) it has been a month and she doesnt think people can change in a month 3) I am only addressing my concerns (getting back together) rather then her concerns (problems we had on the relationship) and 4) her girl trip. The girl trip was a BIG issue when we were together and she has not gone on that trip yet. So people feel she will not make any contact prior to her trip because it was a such a sore subject and it too risky. I have hit rock bottom and know I can and will change. I love this girl deeply and want to do the best actions to win her back. Anyone with advice that has been in a similar situation or any females point of view would be greatly appreciated. FYI she is almost 31 and I am 36. Thank you!