I've been an abuser and I want to move on.
Do you think that this is the best outcome for each person involved?
It is. I can't act like this anymore.
If someone was abused by you then you shouldn't expect them to just move on. You should be punished for being an abuser. You might want to just move on, but that might not be an option for the person you hurt.
If they aren't able to forgive me then I shouldn't make the first move in apologizing.
Being abusive is horrible and you need to apologize and take responsibility for the bad things you did. No one is required to forgive you, but saying your sorry is a start and making efforts via therapy or something similar is critical moving forward.