Make sure neither valve has a heater to cathode
leakage.  Insure the DC  
It used to be common to run the rectifier heater off its own winding, and
tie one end of that (or the centre tap if there is one) to the rectifier
cathode. Then a bit of h-k leakage does little if any harm.
  bus is clean
 as a common old valve gear problem is dried up electrolytics. Try
 grounding the other
 side of the filament  string or float the heater string (insure neither
 side of the heater 
The better power transformers have centre-tapped heater windings
(3.15-0-3.15V). Try earthing the tap (rather than one side).
  winding on the power transformer is grounded.
I've also put a 100ohm 2W pot
 across the heater winding and grounded the slider to be able to balance
 the heater 
Commonly called a 'humdinger' in the UK :-)
  voltage against ground.  If all else fails run the
heaters on DC. 
Certainly for testing. RRun the heaters off a battery. If the hum goes
away, at least you know where it's coming from.
-tony