You could have someone near by operating a cb or ham radio at power levels that exceed what federal regulation allows.
While this could happen, it also could happen with any RF transmitter, operating at any power level and frequency combination, depending on distance and style/directionality of the antenna being used.
EVERY piece of conducting material in your rig, from the wires in your instrument down to the traces on the PC boards in your amp, are antennas. And, of course, they are all different lengths, shapes, and are all "pointed" in different directions. Manufacturers of electrionic devices (well, most reputable manufacturers, anyhow) shield and isolate their components from outside RF (and even internal RF) to make a reliable product, but there's only so much they can do... most devices will be vulnerable at certain frequencies, especially when power levels and antennas transmitting on those frequencies cause the electrical field strength to be high nearby. And the RF picture for any device changes with every physical move, as antenna phasing, shielding from external sources, and exposures to field strengths vary. The problem is, in the amplified music world, that it doesn't take much RF to create a problem, and the likelihood of this being a problem is VASTLY higher in our increasingly wireless world, and also increasingly difficult to track down.
Most hams transmit on single side band, which would not sound intelligible if demodulated by your amplifier.
While many hams transmit on SSB, most do not (probably due to cost of the equipment and the extra effort required lol). SSB would indeed most likely be unintelligible as received and demodulated by your bass rig (unless it happens to have a product detector and a finely tuned beat-frequency oscillator).
The fastest way to solve the problem while you don't have much time: switch out pieces of your rig until the problem disappears. Try different cables, guitars, pedals, amps, cabs, etc. Also try moving thing around. But while doing so keep in mind, depending on the power, distance, and/or directionality of the offending signal, you may not be able to solve the issue easily or quickly.