That is an interesting idea but I think it would ruin the whole bidding war mechanic.  I mean, after spending all that money to outbid a foe who wants the pirates to attack me, it would really be annoying to have my foe cancel the attack on him by a second round of one-party negotiations.  Why even bid at all? I just think it would make hiring pirates all too uncertain to be worth the money.

If I remember correctly, bounty doesn't only go to the pirates, but also can be collected by the player factions, encouraging everyone to attack whatever faction has the highest bounty.  I'm too lazy to look it up, but I think one of the races has research that up the bounty collected.

My idea is that there is a difference between having your stuff destroyed, then rebuilding them (which takes time) and paying the pirates to save your stuff. 

Monetary damage is still there, and (unless the bidding mechanics change) if the attacked player has lost the bidding war, odds are he won't have much money in the coffers.

An alternative could be having a 'bribe' button show up on each pirate ship - as long as some 'pirate ties' tech is developed, for them to be more conversational to you. If you click on that button, you will be bribing that pirate ship out of the fight, It should be a mass-activatable skill (i.e. if you select several pirate ships, you should be able to bribe them all at once).

Oh, and the skill should only be useable when pirates are actually raiding, but not when you are attacking their base, for example.

How about having the option to "pay off" the pirates with an amount of credits equal or proportional to your bounty?