Dear {Recipient},
I know we have had our differences, but I would like to offer you an apology even though our relationship is over. I believe that we both had our faults, but perhaps my faults were more severe in the end. In particular, I am very sorry for the way I {behavior}.
I am also sorry for the bad terms on which our relationship ended. If I could go back, I would try to be more level-headed. Even though I do not think we were right for each other, I would still like to be friends with you. I have always enjoyed your {positive quality}, and I do miss being able to {activity} with you
.
So, I hope you can forgive me. If you'd like to get together some time, please contact me at {phone/email}. It'd be really great to just get together and talk.
Regretfully,
{Sender}