Oh, first of all, Welcomr to the Forum! 'Yours is 2011'...so I gather you bought this used. The symptoms sound like the age-old problem of solder joint fractures...something that eventually happens on gear that gets moved a good deal, from gigs to rehearsals, etc, and Bugera's engineering dept made mechanical decisions that over time results in solder joint fractures, from PCB assemblies being supported by pot terminals, jack terminals instead of mechanical supports...that sort of thing. I looked at the photos on line to see this is a a product with multiple circuit boards, and could be a challenge to pull apart and begin searching for the causes.
With the whole band's equipment powered off of one wall socket in the rehearsal room....I don't really think this is the cause, with the AC mains fluctuating, though hard to say. I've only been inside one Bugera, owned by one of the studio clients where my shop is (CenterStaging, Burbank, CA). Internally in your amp, there would be a power supply regulator to yield stead voltages for channel switching and such. I don't know how much of the tube circuits make use of low voltage analog circuits (IC's, analog switches, FET's and such). Does the switching change without the foot pedal plugged in?
We'd need more info to start diagnosiing the problem(s). Do you have experience working on equipment like this, and equipped with the essential tools, voltmeter, etc? We'd also need a schematic....just to make the task easier, though not impossible without.