Why did I lose money after a bounty was put on me

Call Lester, he will help you put a bounty on other players.

Bounties can be put on you by other players or sometimes by NPC's if you steal their car. If nobody kills you after one full in-game day (48 minutes real time), the bounty will expire and you receive the cash. There's even an achievement to do this.

Spending time in LS Customs does not count toward the 48 minutes. You are best off hiding in your garage or a remote location if playing in a public game. Or if you really want to shake it without the heat, just play in a private game for a while and it will go away once time is up.