The bandits are usually a faction with a name, which can be seen in the "nearest ships" (or enemy) part of your hud.

I would imagine it's either the Corsairs, or more likely the Hessians.
They can be made friendly by shooting the other pirates, or you can pick up bribes for them as well (not sure where to pick them up though!).

If you know who they are, in your person icon you can see what your rep is with factions in the game. Clicking on their name will give you information - who they like, who they are enemies with etc. Generally killing their enemies will make you friendly with them, but of course it will create new enemies in those whom you are killing, and their closest allies.

kill bounty hunters lots and lots of bountyhunters then when your through. you will becomes neutral or friends with all bandits. but you have to kill bounty hunters.

i host the evil empire revolution. a server from north west new jersey. which is 12 feet underground in a lead lined bunker nobody can get to me nobody is going to take me alive.