School me on Old West outlaw bounties

How did they work? Just finished watching Jane Got a Gun and at the end the heroine walks into some shit ass New Mexico town with the bodies of a bunch of outlaws, rips all the wanted posters off the wall showing they were worth like $20k in 1870-something dollars, and walks away with sacks of money.

How does that work? Does that shit ass town have piles of money waiting around to pay bounties? I'm thinking the reality was something different. Just curious how it worked.

But I can't imagine these little Old West towns had the cash on hand to cover bounties. Does that mean the claimant of a bounty had to sit around and wait a few weeks for that money to be stage coached in? Travel to a major hub? Just curious.