Hi Ken
The horrible noise might not be due to a fault in the radio (although I am sure it will have a few faults).
Modern devices use SMPS and these can play havoc on AM radio's reception.
So once "done" it may still make a racket once returned to the owner.
Just worth bearing in mind
Other than that the reservoir and smoothing capacitor seem to reform well on most Bush sets of this age but the UL41 can be a bit notorious for hum when aged.
For what ever reason they seem to fare better (longer quieter life) in sets using a transformer for the heaters than the AC/DC sets.
You may need to change more than just the grid coupling capacitor, many change all the wax paper capacitors on sight and if its for someone else this may be the best approach.
Nice sets they sound pretty good.
Cheers
Mike T