1838, "anything large or exceptional; a man of great strength," American English slang (originally Missouri/Arkansas), perhaps meaning something that takes one's breath away and thus 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's definition, probably not the way they would have explained it in old Missouri and Arkansas), which might have influenced it. As a generic or playful address to a male from 1948, American English. Meaning "horse-breaker" is from 1891, American English; hence the back-formed verb bust (v.) "break a horse."
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