I put a new pickup into a p-bass recently, simply replacing the two wires from the pickup in the circuit, and putting the pickup in place.
In most situations, it works as expected- through my practise amp it is normal, but when I have used it through my live rig it hums when the volume is turned down. I have used that same rig for some time, and it doesn't produce this problem with any of my other basses- likewise, the bass doesn't have this problem with my other amp. So it is just that combination which seems to produce this noise.
Any ideas as to what might be causing this?
'My Sound? Hell, if I can hear myself, that's my sound!' -Carl Perkins
Im sure way more experienced people on here gave a better answer to that then I will, but here are a few things that crossed my mind when I read your post.
What sized soldering iron did you use. I was thinking with a high enough wattage you could have done damage to the pot you soldered to. Another thought. open it back up check for solder flash. maybe a little spot touching you to ground or close enough to pick it up.
One more thought I had. do you have it installed correctly. (polarity, closeness to the strings, etc..
Last thought I had. Maybe the pickup is just defective.
Here is the part where someone will jump in and give you the real answer