If the relationship was ending, she should have told me that we needed to break up. It takes two to start one, but one to end it.
Maybe from casual observation or maybe from listening to too much Loveline back in my day, but often it seems some people just need to be in a relationship which means that don't break up when they should. They wait until they have another one to jump into. I saw this with a couple of my female college friends as well, they were very unhappy in a relationship that was not working but never broke up until they met somebody new. Not to say yours was a horrible relationship, but some people just hate the idea of not being in one.
I want to reconnect with my ex because I love her and I'm going to try being friends. Maybe I'll tell her all of this. I don't know.
This can sometimes work, but you really have to give it time and let it form naturally. If it is one or two months, don't push it as I think it is way too early. Let things be for 6 months or a year or more and then sometimes it can work. The couple of ex's that I later became friends didn't happen by trying to make it happen. One I tried to remain in touch with and the more I did the more distant she got. She had her own things to deal with and pushed me away. Maybe 6 months later we reconnected and now have been friends for the last 10 years. I have met her BF,, stayed in their spare room, taken them to dinner when they were passing through Singapore one year, etc. Maybe we chat every few months now but I know she will always be a friend.
The other ex-gf really despised me for a while and didn't talk to me for years though we did have some common friends. After a couple of years we bumped into each other and had a casual conversation and started to chat some. Then I decided to move overseas, so we met a few times for dinner and became pretty good friends at that point. If I was back in town, we met up and she gave me a couch to sleep on if I needed it. All was good until one of our common friends later destroyed it again by suggesting I had other motives but that wasn't true. So when she said she no longer want to remain in touch, I just let it be.
Sometimes it is just not worth the energy and your peace to try to force a situation to happen. It is beyond your control so relax and wait to see what happens.