Weird! I found this article by someone who thought the same as I did. The term being "my bag" must be some strange urban legend:
Dear Word Detective: I hope you can settle an argument between me and some younger co-workers of mine. I am 33 years old, and to the best of my knowledge, the term "my bag" means "my fault." You step on someone's foot and you say, "Oh, my bag." It seems that everyone at my job under the age of 20 or so believes that the term "my bad" would be the correct phrase. Of course I explained that I believed that the term was taken from "caught holding the bag," meaning the one who took the blame, hence "my bag" equals "my fault." Please clarify. -- Keith, via the Internet.
Well, Keith, I hate to say this, but I'm afraid the kids are right. I wouldn't be too disturbed about this -- after all, even a broken clock is right twice a day, and all that.
To be honest, I wouldn't be so sure about this question myself were it not for the fact that there was recently a protracted discussion of "my bad" on the e-mail discussion group of the American Dialect Society (which is an organization of scholars who pay attention to such things). "My bad," an exclamation meaning "my fault" or "my mistake," evidently arose in the mid-1980's among players (primarily Black) in informal "pick-up" basketball games. One player would throw a bad pass or flub an easy shot and say "My bad" as a sort of handy shorthand for a more elaborate apology. The term's transition to more general slang use was apparently greatly accelerated by its inclusion in the enormously popular film "Clueless" a few years ago.
As to "my bag," it's been slang for "personal style or preference" since the early 1960's, but I've never heard it used to mean "my fault." And "my bag," which comes from the slang of jazz musicians, is unrelated to "holding the bag," which dates all the way back to the 18th century.
Robb