“I’m sorry…” is commonly a blank check. Basically, it tells the other person that they can count on it happening again. People will have expectations about what it takes to clean up the mess. The strategy I suggest is to first take authentic ownership and responsibility for what we have caused.
It may be wise to consider some reasonable ways to create recovery before asking what can be done to make it right, yet be prepared for it to not be enough. If you are sincere and have checked your plan with someone of wisdom, it’s no longer about you.