Busted is a slang expression? Yes. So 'buster' means loser? No.

Buster is a nickname for any male; can be threatening depending on tone of voice and context, as in, "You better watch it, Buster". You see a small boy committing some mischief and say, "Well, aren't you a little Buster".

Busted is a shortening/slang of burst. The bottom burst out = the bottom busted out. Your bicycle is wrecked = it's busted. Hopefully, a person will not bust--though his/her finances (for ex.) may go bust.