When speaking with the bartender, you will learn that the port authority sells 25 crates of silk to pay the bounty. Unless you are short on cash, do not turn in bounties until the price of silk at the port you are at is high. Note: The highest silk can reach is 4,800 gold.

Once you have gotten a sizeable fleet, you can start hunting notorious pirates for bounties. Each bounty is not worth all too much by itself, but it seems to be greatly multiplied when you turn in multiple bounties all at once.

Ask the Port Authority for news. You will learn which ports the wanted captains are going between. Once you have a fleet strong enough to take on the pirate fleets, start plying your way between them for big money. You will get the bounty plus whatever you get from defeating the fleet.