The pirates usually have only a single base. The chosen victim's planets may only be reachable by sending ships past planets you have taken control of. In that case, try to restrain your defenses from destroying the pirates - take out jump inhibitors if they are holding the pirate raid in your space.
If you lose a trade station to these "passer-by" pirates just rebuild it in a different part of the system.
On some maps it can be worth picking the pirate victim purely based on the route the pirates will take, just to make sure they don't clutter up planets you are hoping to take over yourself.
As for the bidding - the trick is to back two horses. If your own bounty is third or lower in the list then the two top players will usually bid on each other instead of you because that will be cheaper (doesn't always work with humans - they'll team up on you instead). Using that technique you can usually decide who will "win" the auction while spending relatively little money yourself. Also, if there is fighting going on make sure you keep the bounty high during the auction - it will decrease every time a ship is destroyed and that can easily waste your bounty money if you put it on too far in advance.