Not an entire campaign where the only or main thrust was bounty hunting, but one character in the party, a Ranger, was a bounty hunter, before he was killed in combat.
In my world the Ranger is more like a Frontier's Lawman. Often they work alone, especially when hunting. He also worked for the Byzantine government so he would hunt for them sometimes, sometimes hunt for bounty, and sometimes just hunt criminals and outlaws and invaders and Dragoons because he was good at it and wanted to and it was justice to him. These situations made great "lone adventures" although occasionally the Ranger would work with the Basilegate, or the entire party. If the mission was big enough, or the he was ordered to by his employers. These situations almost never involved an entire caiman, but hunting down others, for bounty or otherwise, was often a big part of some campaigns. For instance once they spent a large part of a campaign hunting down Goth raiders who had kidnapped an Abbot's niece, and were enslaving people, and they were paid handsomely for it by the government.
In the very first world I ever created a Lich employed three brothers (one was eventually killed by the party, the other two hunted the party for years) to hunt and harass the party. The brothers actually assassinated a high level player character (brother of a Paladin) in the party, crippled one up so bad he had to retire, and badly injured a couple more. The brothers paid lots of different third party agents to do their work for them, and every the party was sufficiently crippled or hampered the Lich paid bonuses to the brothers (usually in the form of magic, some rare service, and antique or valuable item, valuable information, and occasionally in hard treasure - but he paid bounties in other ways because slowly over time he was enslaving hem psychically and transforming them magically, so his bounties had a double intent). Eventually the party had enough, found out who and what was hunting them and went after the brothers. That led to a really nice set of encounters, combat and otherwise, between the brothers, the party, and eventually even the Lich. That set of campaigns turned out really nicely. Though also deadly for more than one character and NPC.
Bounty hunting done right makes for good adventures and campaigns I think.