What kind of bass is it? It sounds like a microphonic pickup!
I've found that, generally, bass pickups are more microphonic than guitar pickups. Bassists tend not to use a lot of gain, dirt and drive (very generally speaking). I've even found supposedly epoxy potted pickups, made by a manufacturer that rhymes with Bimarzio, weren't actually epoxy potted as much as epoxy capped; with the coils still floating in air inside the pickup covers.
When I was in a noisy 2-piece band, using lots of distortion, I was surprised by how many stock and aftermarket pickups squealed at volume.