IS IT NORMAL THAT MY BRIDGE PICKUP SOUNDS LIFELESS?

You're losing volume when you turn up both pickups? Sounds like phase cancellation.

If you don't like the way a bridge pickup sounds, it might not be the right pickup for you, or you might just need to play with the pickup heights to get it to sound the way you want.

 

I'm with FMB.. you have a wiring issue of some kind. If you post a pic, one of the grizzled veterans of this forum might spot the issue right away!

 

What guitar do you have (specifically)?

I got a 2003 MIM P-bass with a PJ setup same as you describe and pretty much the same observation, the bridge pickup is lifeless, I'm pretty happy with the neck P pups, but would like more out of the bridge J pup.....

Wondering if rewiring for parallel/series ability would help, or just swapping it out for a "better" pup.

I am assuming the guitar has Fender OEM pups installed.

Could just be poor wiring, from what I hear the MIM wiring is sometimes suspect and needs some resoldering and swapping pots and caps.