Green’s Dictionary of Slang

duster n.⁴

(US black) the buttocks, the posterior.

1946		Mezzrow & Wolfe Really the Blues 199: Dig you later, Paris old gal. Keep on wriggling your saucy duster and smelling sweet.
1972		B. Rodgers Queens’ Vernacular.
1984		W. Diehl Hooligans (2003) 413: I’m tired of sitting on my duster back here.
1989–2003		R.O. Scott Gay Sl. Dict. 🌐.

In phrases

on someone’s duster

harassing, persecuting someone.

1972

(con. 1920s) in J. Curry River’s in My Blood (1983) 166: He was really on my duster from then on, and I got off at Memphis.