From The origin of 'my bad':
The best evidence obtainable at present points to Manute Bol (above), the 7'7" Sudanese NBA player whose native tongue was Dinka, as the inventor, sometime in the 1980s, of this now–ubiquitous phrase.
Finally, someone to blame for this incredibly hard-to-hear phrase. Yeay. I keep wanting to say "my bad what?", since my and bad are both adjectives there to my ears.