I think a genuine apology is all that is necessary, and not one that is shrouded in resentment.
Apologize profusely, and promise to not let it happen again. If her mom lectures you or yells at you, avoid rolling your eyes or becoming defensive in any way. You were wrong, and you know it. Try doing something novel, like bringing the girl home EARLY the next few times you go out, and don't be late again.
Relax... I'll need some information first. Just the basic facts - can you show me where it hurts?