It may be part of the humour, but is it the normal view taken towards such people? No matter what their motivation, if it gets criminals off the streets and behind bars, then it should be applauded rather than condemned?
I have a feeling that to many the bounty hunter is seen as being not much better than those whom they pursue, tantamount to vigilantes; when you combine this with the idea of the romantic outlaw, which is also a staple of the western genre, then the bounty hunter can often be thought to be in his own way a bad guy.
Take the case of Robert Ford - immortalized in song as “The dirty little coward, who shot Mr. Howard”, Howard being an alias of Jesse James. Ford was an outlaw in James’s own gang, who then conspired to get the bounty on James’s head - and so keen were the authorities to have him do it, that they threw in a free pardon as well as the $10,000 reward.
It can be seen from the popular ballad, from which I quoted, that Jesse James was the one held in high regard, and the bounty hunter was the “baddie”. Similarly, Pat Garrett often comes off worse in folk-lore than Billy the Kid.
Bounty hunters also operated on both sides of the law (at least in stories): they could be thought of as how Boba Fett is shown in the Star Wars films - prepared to track a person down for money, no matter who was paying, and whether they were in fact guilty of any crime or not.
It wasn’t until quite late on, in 1954, when Randolph Scott played the title role in The Bounty Hunter
that Western cinema took the bounty hunter to be upright, moral and true - characteristics which had more frequently been given to the outlaw, in the manner of Robin Hood.