...I am in the UK and bought my d350 from the USA...
Only difference with USA is 230v/50hz mains.
Okay, I went back and reviewed a few of your posts on this. I am under the impression that this amp uses a universal power supply that adapts itself to the voltage (and, I would presume, line frequency) of power available in different countries. If this is true, then, aside from maybe coming bundled with a different power cord, I shouldn't think an amp sold in the UK would differ physically from one sold in the US. (And, if it did, that you'd have issues regardless of what you were doing with your bass.)
I could be wrong about this or missing something. @agedhorse would be the one to confirm or correct these assumptions.
Definitely not on my d800...or my d800+ di pedal into the aux in on the d350. Using same power chord on both amps...not simultaneously obviously!
Interesting (suggestive) that you don't get the hum using the D.I. into the aux-in.
If everything is the same but the amp (or preamp), that would suggest that something in your D-350 is causing (or allowing) this to happen. The question, then, is whether this is unique to your amp or some inherent difference between the D-800, DI pedal, and D-350. (I could be missing something here, as well, but this is how it looks to me.)
Tried a Gibson jazz guitar, single pickup *humbucker passive with only one volume control at a gig today. When you back the guitar volume control off a bit hum appears, just the same as my basses switched to passive mode...
A further question would be whether there's some freak wiring issue in your home or rehearsal space causing some interaction with the amp, but your experiencing it at a gig, as well (and with a passive humbucker, noted), seems to make this less likely.
Can you get your hands on (or visit a store with) a second D-350 to try alongside yours?
I'm curious as to whether anyone else stateside or in the UK have experienced similar, and if it varies with location/voltage/line frequency, if so.
Hope you're able to get this sorted.