I hope you can contribute to a discussion I've been having with my friends. When I was in high school ('84-'88) and maybe even a bit before that, I remember an expression people used to use to accept responsibility for something, "my bag". For example, "Oh! I scuffed your Air Jordans! My bag!" By the end of high school many people were using the slang in a way I thought was incorrect, changing it to "my bad". This always sounded to my ears like uncool people trying to use street slang and getting it wrong. But now and for so many years, "my bad" has been in use by so many people that I have trouble getting anyone to remember the original "my bag". I've had people tell me it's a Michigan thing (I grew up in Kalamazoo) but I've also been told by many old classmates that they don't remember "my bag" having this meaning. Can you shed some light on the origins of the expressions "my bag" and "my bad" and on their relationship to each other?
I had never heard "my bag" used the way you say, Doug, so I Googled it and found that there are many many people asking the same question you are asking. I read a lot of comments as well as Urban Dictionary about this and here are my own conclusions.
Using "my bag" for "something I prefer" probably began with jazz-men in the early 60s or earlier and quickly was picked up by hippies. Using "my bag" as a way of taking responsibility began in the 80s. Urban Dictionary indicates it was in Michigan as you guessed. I can see a connection between these two usages. They are both talking about something that is part of one's personality. The earlier use is really more than just a momentary preference, it is long term and comes from past experience. The latter use is an apology for a personality flaw.
This connection is my own idea so you can take it for what it's worth.
The use of of "my bad" seems to be a completely different thing. Rather than talking about one's personality, it is simply an apology, "I'm sorry I did something bad." I could not find a date that this phrase began but I have heard it for maybe 20 years or so. There may be a connection in the past but today, if they are used properly, they mean different things.