From the Urban Dictionary: bust on:
(1) To beat up or to physically attack
(2) To verbally tease or skewer someone either in a joking or mean spirited fashion with the intention of embarrassing or humiliating them; similar to “cracking on” someone.
They bust on me because I came to work with two different shoes and didn't know it.
I would suggest it's probably the second definition.
c.intr. to bust on: to attack verbally, to criticize or scold; (in weakened sense) to tease, to mock. Also trans. (without on) in the same sense. Cf. to bust (a person's) balls [...]
1961 Press-Telegram (Long Beach, Calif.) 14 Dec. b8/3 Don't bust me means quit kidding.
1987 N.Y. Times 19 Dec. 51/2, I used to be real bad, always busting on people and clowning around.
1996 D. London Sun Dancer (1998) i. 12 ‘Relax, Clem, you got the pants,’ Elijah said, without looking up from under his ten-gallon. I laughed. We were always busting on Clem's pants.
2006 K. Hnida Still Kicking viii. 139 We..spent a lot of time busting each other about how bad each other's high school team was.