Hi,
In my opinion, it depends on the level of the offense or the many times one has offended the other person. I am perhaps at the other side of the problem. I have a brother with behavioral issues and many people including me are just tired. For me, an apology from my brother will not be enough. I am having a lot of problems to forgive my brother despite I suspect there are reasons behind his lack of control that he cannot control for the moment.
If i could offer the perspective of somebody that has been (repitedily) offended by somebody that has behavioral issues I would like to see this person not only apologizing but assuming full responsibility of his acts and looking for help to overcome his issues. Otherwise, what I really want is to get away from the person. I do not think my brother or any person with control issues are bad people at all. But I think they have to do something to improve. They have to be proactive.
Sorry if I am blunt, I do feel your pain, but also I acknowledge the pain you may be causing. I have faith there are solutions and you will be able to tackle your impulses.
A big hug