I dont know what your bridge pickup is, but on some models, there is a seperate ground wire in addition to the sheild wire that is hooked to the pickup chassis. If you have such a wire, you may need to star ground that as well.
If you have the braided single conductor wire make sure your braided cable is soldered to the base plate. Sometimes the joint is cold, or broken in a way you can't see. I've had a couple come through that were just not soldered at all.