My bad originally came from the term my bag.
This was a term used when playing a game of spades (a common jail house or hood game with cards) In the game you would have to fortell how many "books" or hands you would take. If you went over that number it was called a "bag". If you were playing with a partner, which was mostly common, it is considered a courtesy to claim your mistake by saing "My Bag" or get shot.... : ) your choice... anyway this carried out to the street and stupid beverly hills bitches misundertood the ghetto term and said "My Bad" and it stuck in mainstream pop culture.