I've gathered a bounty that I can't afford to pay off. What do I do?

Your only options for clearing a bounty are either paying it off, or surrender and go to jail. The latter is only possible when your wanted level is low, so if you've been shooting up some law enforcement you will likely be shot dead if you surrender. To clarify: there is no decay or decrease in bounty over time!

When you surrender, you'll have to wait out your sentence in jail. This page claims that you could be rescued by friends whilst your in jail, but I haven't seen that happen myself. Granted, I haven't spent a lot of time in jail.

To surrender (from IGN Wiki):

If you bounty is low enough, you can sometimes simply surrender to the nearest lawman before things escalate by targeting them and pressing Y or Triangle to surrender, and putting away your weapons. You'll spend a few in-game days in jail, and the fine will be paid automatically.