I would take this opportunity to explain to your son that there are consequences for his actions and that if he isn't nice to other people, he wont be allowed to play over. He now will have to earn back the trust of the other boy and his mom before he is allowed to play over.
Your post makes it sound as though there was an ongoing problem if your son was bullying last year, rather than an isolated incident. So I'm not sure it's an issue of second chances.
I know there are kids in the neighborhood that I wont allow to come into my house without their mom present. It just isn't worth the mess and the heartbreak over broken toys. The only difference is that I don't tell my sons that certain kids cannot come in the house. If one of those kids show up, I suggest that they play outside or call the mom and make other arrangements for a later time. Then I invited mom and son over to visit or arrange to go to a park close by.
Maybe the mom will still allow them to play together if you invite both mom and son over to your house and your son shows that he can play nicely.
My community is about 50% Mormon and I have found them to be very open to having our kids play together. My son was invited to the baptism of all his friends when they turned 8. He is involved in Cub Scouts through a non-LDS unit and has invited some of his LDS friends to join us on other Cub Scout outings, and the parents have always allowed their kids to come along.