Meaning of "bust on somebody"

It means to harass someone or give them a hard time, in a friendly or "friendly" fashion. I believe JeffSahol is correct, that it's related to the usage "to bust someone's balls". (Neither usage actually requires that the person have the sexual anatomy in question.)

According to the Oxford English Dictionary, to bust on means:

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 at ball n.1 Phrases 5c.

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1961 H. Ellison Gentleman Junkie 88 Some joker busted on Kurt‥telling him the eggs were greasy.

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.

So it has been linked to the American English slang of "busting someone's balls", which they suggest might be linked to Italian:

Perhaps after Italian scocciare le palle to bother someone, lit. ‘to break someone's balls’ (or perhaps ‘to bother someone's balls’) (a1863), also rompere le palle, lit. ‘to break someone's balls’ (1972).]