I have the same situation in a jazz band, with my custom P-style bass. Here's what I did:
1) Get a set of the new reforumulated Fender flat strings, the 9050L, 45-100. They have been reformulated to have a little more growl and not just the hollow thud of other flats. I personally like a 105 on the low E, and I found one. I've also been told that word on the street is that a new set, the 9050CL, 45-60-80-105, will be available after the new year. They really helped improve my tone overall for my jazz band.
2) Leo Fender originally attached a block of foam rubber under the bridge cover to deaden the sustain and give more of a double bass feel to the decay of the note. It works. I actually have a vintage style bridge cover reinstalled over my bridge with small blocks of foam rubber shoved in so I can adjust them as necessary.
The first rehearsal I played with the band after I did this locked the band into the groove much better than before, even though I've been playing with them a couple of years and the only things I changed about my setup are what I have listed above.
1) Get a set of the new reforumulated Fender flat strings, the 9050L, 45-100. They have been reformulated to have a little more growl and not just the hollow thud of other flats. I personally like a 105 on the low E, and I found one. I've also been told that word on the street is that a new set, the 9050CL, 45-60-80-105, will be available after the new year. They really helped improve my tone overall for my jazz band.
2) Leo Fender originally attached a block of foam rubber under the bridge cover to deaden the sustain and give more of a double bass feel to the decay of the note. It works. I actually have a vintage style bridge cover reinstalled over my bridge with small blocks of foam rubber shoved in so I can adjust them as necessary.
The first rehearsal I played with the band after I did this locked the band into the groove much better than before, even though I've been playing with them a couple of years and the only things I changed about my setup are what I have listed above.