Are you going to tape by chance? Could this be crosstalk? If so the only likely solution is to overdub the Bass. Pickups can be microphonic to an extent. Maybe just putting the bassist in another room would do. Just taking stabs in the dark here.

It's not tape

If I put the bass in another room and play the drums there isn't any bleed, it has to be the pickups or the body of the bass resonating to the drums. I'll have to record it after or play it in another room

Thanks

Put some isolation gobo panels around the bass player!

no possible way that your bass when going direct is picking up drums?? i NEVER have that happen and i only record live 99% of the time. maybe you should just have the bassist in the control room when tracking and go direct, its punchier anyway.

It absolutely can happen. Pickups can become microphonic - usually not high quality ones, but I've had a few basses that exhibited symptoms that I could see becoming a problem, as described above.

Have you tried checking out the bass itself? Plug into an amp, set the gain high-ish, and tap on the pickup covers. There should (in theory) be almost no sound generated, but you'd be surprised how much signal you can get this way with a faulty pickup design.

If the bassist is dead set on using that bass, one thing to suggest to him/her is the good old dip-it-in-paraffin treatment. Sometimes the problem lies in the coils looseing from the bobbin, this solidifies things back up. It's a pain, but weighed against the benefits of having the bassist and drummer playing in the same room together (if that's how they prefer tracking) it may be worth the effort.