1838, "anything large; a man of great strength," American English slang (originally Missouri/Arkansas), perhaps meaning something that takes one's breath away and an agent noun from bust, v.. Around the same years, buster (as an extended form of bust (n.)) also meant "a frolic, a spree." Hence "a roistering blade" (OED; probably not the favored definition in old Missouri and Arkansas), attested from 1850. As a generic or playful address to a male, from 1948, American English. Meaning "horse-breaker" is from 1891, American English; hence back-formed verb bust (v.) "break a horse."