Just don't bid. 5 turrents and a repair bay or two was enough to hold off the pirates for an entire game for me. This was on Razor's Edge and they were attacking the same planet every time.
The way I look at it is this, most people probably only bid on the pirates so that they themselves arn't attacked. So they are only going to bid the least amount required to win. What I've read online makes it sound like the higher the bid, the more pirates which will attack. Keeping this in mind, if you get into a bidding war and lose, instead of only 250 credits worth of pirates to deal with, you are now having to fight off 5500 credits worth of pirates and you wasted 4700 of your own credits trying to win(random numbers there). If you hadn't bid, then you ot only would be saving your own resources, but you would only have to fight 250 credits worth of pirates.
Sometimes I will bid on the pirates to keep them away from a team mate who is not doing very well, but I prefer to just not bid on them at all and save resources.