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It's the Wild West you'll "earn" enough to pay them off if you do some of the story missions.
Also if you don't want to ride deep into a territory with a big bounty on your head to pay it off you can go to any on the post offices on the map and pay from there, helps avoid bounty hunters attacking and forcing you to jack the bounty even higher.
in other RDR2 news, found myself in the middle of some real hill have eyes shit with almost no visibility. scariest game sequence for a while (well since I first encountered wolves by riding into 3 packs at once and being chased across the map by over 10 of the fuckers.
Ransoms dont go away so you'd have had to pay it at some point.
only way out of it is to get caught with less than the bounty money on you (need to commit a minor crime to have the option to surrender) and they'll take all you've got and lift the bounty when you leave jail.