tough call, I still might be tempted to put it back in there.
No. Don't ask for forgiveness at the end. All you are doing is taking responsibility for your part of the problems in the MR, and showing her that you understand her hurt, how you played a part in that hurt,that your working on bettering yourself, and that you'll be a safe person to come to if she wants to talk in the future.
You can ask for forgiveness later in a face to face. But remember, forgiveness is not nnecessarily something thats JUST for you. It's for her too, it plays a huge role in the healing process for the "hurt" party. Sure, it'll be nice to know that your apology was heard, and accepted, for you, but if she doesn't forgive, it'll be something that she drags around with her for the rest of her life... A problem my W is dealing with now from holding grudges and not forgiving her past troubles.
Apology, Acceptance of that apology, and forgiveness are all separate things that come at different times.
