First, unplug the bass, play it and see whether you hear any buzzing at all. Listen around all the hardware to see if a problem is localizable.
That's probably not your problem though. More likely, you're getting electromagnetic interference from something in the vicinity of your rig. You want to debug this by trying your entire rig somewhere else (not just the other side of the room) first. You should also try plugging into a different amp.
When you hear high-frequency grit or distortion, this is usually a byproduct of electronic noise that's outside the range of what you can hear or what your amp can reproduce (by the time you're through the speakers, a regular bass amp has output over less than 1/3 the full range of your hearing). You might be picking up noise from lighting, computers, cell phones, radio, or something else electronic in your vicinity. The preamps in the bass have very wide frequency response, well beyond what you can hear. They will happily amplify ultrasonic signals and do so until the preamp is totally overdriven. The effect of that overdrive is that the audible parts of the signal, especially the treble becomes distorted as well. The problem you describe with a feedback point on the tone controls is also a symptom of the preamp being overdriven by something you can't hear.
This can also be caused by a bad interaction between your amplifier's front end and your bass. Trying a different amp and different EQ settings may make the problem go away. If that's the case, then you really will probably need to switch amps to solve this problem. The Q switches can generate a LOT of boost at their frequency centers when the Q switch is in the high position. It would be surprising that you'd get feedback like this with a normal bass amp unless you were playing really loud or in physical contact with the amp.
If you still have the problem with a different amp and different location, then something really may be wrong inside the bass. You might look for a dirty connector (you can fix this by plugging and unplugging the molex connectors on the EQ boards) or possibly a short. A dirty connector changes the impedance of the connection and may cause feedback type effects. I doubt this is the problem too as a Series bass has independent preamps for each pickup and the humcancelling coil. You'd need to have developed dirty connectors on all there connections to have the problem on both pickups.
Good luck