Here is a blurb on bounty hunters in the US:
Bounty hunting is a legitimate business and an integral part of the American justice system. Find out how bounty hunting works and follow bounty hunter Bob Burton on the search for a fugitive.
I forgot extradition, bounty hunters do not need to go thru that process, their hunt can cross state lines.
A really fun movie about a bounty hunter is "Midnight Run" (not to be confused with "Midnight Express"!), highly recommended.
In the blurb above they mention a couple of TV "Reality Shows" about bounty hunters. 'Dog' the Bounty Hunter made a name for himself by going to Mexico and capturing the rapist heir to the Max Factor fortune, and embarrassing the FBI in the process:
The fugitive heir to the Max Factor cosmetics empire, Andrew Luster, was living a modest life in a Mexican seaside resort for about a month before he was caught by a team led by legendary bounty hu...
The Mexican govt held him for several days on kidnapping charges! That made Dog a minor celebrity in the US, and he had a long running TV show.