Is it possible ?

The option is being considered Right now, you can't, but in the 1.02 patch they're adding 2 new maps with no pirates on them.

They will be releasing a patch shortly (few days?) that will add maps that don't have any pirates. They will also increase their spawn rate which will also help alot for those struggling with the pirates.

As a more general note, you shouldn't go frenzy on the pirate bounty raising.
At the start of the game, the pirate fleet is incredibly small and really easy to kill, so if someone puts money on you, you should consider just dealing with the pirates rather than starting a "bidding war".

In addition to that, you should only put money on someone's head once the timer reaches 0:00, it'll be at 0, this way you can avoid a "bidding war" and thus have to spend less gold.

Happy pirate hunting!

Isn't it too late once the timer reaches 0:00? I assumed you had to do the bidding before that, and at 0:00 the pirates set course for the unfortunate looser?

Nope, the 0:00 is meant to be a close estimate, but you still have a random time variance after it hits 0 and before they launch to up the bids It's usually not very long, though.

I've had it take over 30 seconds before they actually launched.
I'm guessing it might have something to do with the bidding that is going on, when there's a large amount of bidding happening, I think the pirates hold off a little, the more cash the better .