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1.
A word derived from Jamaican slang and dancehall music -refer to macka diamond and blacka song "bun him"

It means if your boyfriend or girlfriend has cheated on you, you should do the same.
If bf/gf has given you "bun" or you are interested in giving gf/bf "bun" it simply means to cheat on them.

*the right definition*
Girl: Mi caan believe mi man gimme bun wid dat dutty gyal Sandra

Girl 2: My girl nuh cry bout dat but nuh "bun him" bac jus gi him di bakery and dun

- simply meaning don't just cheat on him might as well get pregnant while your at it =D
by real j'can January 26, 2010
 
2.
Coined by a popular dancehall song of the same name about lighting your boyfriend on fire after he cheats on you or abuses you.
Can be used in any situation to express dislike in a person, place or thing.
Derived from the patois word bun which means to literally light something on fire.
Gyal 1: Mi man be cheatin, weh mi muss do gyal????
Gyal 2: BUN HIM!!!!!!!

Mike: Man.. my mom won't let me go to the jam tonight..
John: Ah fuck that, bun her!!
by Mr.Vincent! April 26, 2006