Originally Posted by ok321go
Bob was so apologetic and makes no excuses, though he did say it was an 'accident' and is deeply regretting it.
How do you accidentally have sex with someone? Whoops! I slipped and my penis fell into your vagina?
Perhaps you mean, it was a mistake? In which case, to err is human. I'm big on forgiveness... it does no one, especially yourself, any favours to hold onto resentment and anger. The important part is that he realizes both the mistake, and the circumstances leading up to it, so that he'll know how to avoid it in the future.
So you've already ended the romantic relationship, and you're wondering if you should be friends. I don't see any reason why not, if you feel you can trust him as a friend. You're no longer involved in his sex life, so if he cheats on Alice again, that's between him and Alice.