Randomly, certain pirates will have bounties tied to them. There's no way to know which ship has a bounty until you killed it and a bounty received message appears. Bounties can also appear as missions and transponders, that once hacked, sometimes update your system map with bounty locations.
*You can also scan ships in space to see if they have a bounty attached or pay bartenders for tips.
Edit* Thanks to Holmkvists