Yeah, i have a zoom H4N, if I run It on batteries there's some noise with the single coil with the volume past the middle and the tone pot boost that noise (not that bad to be honest since It Is manageable, but getting rid of It would be nice), but if i run the recorder with a power supply the same buzz that comes trough the amp appears, so i guess that i have both problems lolNote that, if the interference is coming through the mains, hum-bucking pickups and shielding won't help that much. Power conditioning won't help if the interference is in the realm of RF. I recommend that you locate the source(s) of the interference before dumping a bunch of money and effort into solutions that may or may not help.
Do you have a way of listening to your bass through a battery powered setup such as a battery powered pedal preamp? If there is no interferences with that setup, it's probably coming through the mains. If there is, it's probably RF.
The technician is going to give me the bass tomorrow, i hope It solves the single coil hum problem, and i'm looking for someone with a power conditioner so i can test if the buzz go away with it :/