bust me down 

means leave me some of that cigarette.

It means please give me your cigarette after you've smoked half of it

means let me have a few puffs of your cigarette

"Bust me down on that stog."

bust me down by Atul May 1, 2006

bust me down? 

A question you might ask a close friend when that friend pulls out a cigarette if you would like to share a cig with that friend.

- a couple second after friends pulls a cigarette out of his poket-

"Hey bro, you gonna bust me down?"

bust me down? by Josh Harris (slang creator) April 24, 2007