There isn't a good way really. Know people in lots of different areas, and ask them to tell you if they see somebody. I suggest a rair hauling route with lots of sectors and your loadout tuned for bounty hunting rather than hauling. You'll make money hauling, and you visit pirate hot spots.
I thought about starting up an out-of-game toold where people could report bounties/locations/ships for bounty hunters to chase (ie. trader sees 500k bounty on a player, makes it to dock, posts that on the board). As a pirate it would be rather counterproductive, but also fun.
The next thing you need to know is how to hunt for a bounty. It is very easy to escape in this game, so you often will only have one chance. The other thing to remember is that pirates have quite a strong interest in their local surroundings ('cos piracy), so if you hop in in a Python, for example, you may find your target jumps out before you can even interdict him, so a Cobra/Viper/Asp may be a better option. Maybe bring friends. Other ways apart from interdicting exist, of course, to take players down, and these IMO are much more likely to work out well for you.
The fact that a large number of pirates are cowardly and pay off their bounties doesn't help. I think bounty hunting players is pretty much the hardest occupation in the game, so good luck.