There is no good response. I would have said see ya. Once a cheater always a cheater. It takes a bigger person to respect them self and walk away from it. He will do it again as long as you let him. Guy's like him kill me. Sorry but I cheated. Is everything OK now? He needs to go. I know its hard and you hurt. You can pick yourself up and start over and meet a nice faithful guy. It just takes time and you can do it! You could always cheat on him and tell him Sorry. No, don't do that. That will make you look bad. And, you are not a bad person, you just had a bad person in your life.
A better response? short of Begging on hands and knees? or breaking down a crying at the thought of losing you? Not much. It's not to say you shouldn't give him a second chance, but make him earn it. if the only thing he did was say I'm sorry, don't bother with him, if he actually pleads for your forgiveness, give a chance, but keep him on short leash.
If he doesn't make it a point to end it with the other person WITH YOU PRESENT to hear him end it, show you he is accountable, go out of his way to show you how much you mean to him and how special you are, and be willing to apologize REPEATEDLY and discuss what happened with you openly and honestly - then forget it, he's not sorry. And he sure as hell isn't willing to change.
Well when Kobe Bryant cheated he got his wife a $5 million diamond ring.
I'm gonna assume your boyfriend doesn't have the income of a pro basketball player but he could have done a LOT better than a simple "I'm sorry". He should be groveling and kissing your ass if he expects to keep you (but I still think you should leave him anyway).