The term “my bag” was common from 1930 to about 1995. It means “my mistake, my fault, my apologies”. The popular term my bad
is actually a 1980s mispronunciation of the term “my bag”.
“My bag” was a phrase used when playing a game of spades. In the game, you would have to for-tell 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 it was a courtesy to claim your mistake by saying "My Bag".
Spades came out of the Midwestern United States in the late 1930s. It was said to have been invented by college students who enjoyed both Whist and Bridge. They were looking for a fast-paced game that was competitive and strategic. The game slowly spread to other college campuses. It didn't really take off until WWII brought so much of America's youth into the military. Because the game was portable, could be played by small groups, and could often be played in less than twenty minutes, its popularity mushroomed. You can still find the game online.
“My Bag” meaning “My Mistake” should not be confused with “Not My Bag.” meaning “Not My Thing.” or “What's Your Bag?” meaning “What's Your Problem?”
When I was in high-school in the 70s “my bag” meaning “my fault” was very common. Even though “my bad” is said to have come out in the 80s I had never heard it until sometime around 2008 or so. I can't recall the last time I heard the term “My bag”.
My bag or My bad, I thought I sent you an invitation.