It certainly could be a sheilding problem, do any other instruments you plug into this amp have hum problems?
if not then it is likely that it is the Bass or your lead that has some issues. Try swapping out your lead and see if this affects it, if not then it could be your sheilding or a connection to the sheilding.
Is the hum affected if you place your hand on the bridge, strings, or the pole pieces of your pickups? if so then you may well have a problem. The bridge and strings are usually grounded by a wire that feeds from the bass of the bridge to the common ground of your volume or tone pots which are all commonly grounded to the Jack ground. If you have access to a Voltmeter set it to a low ohms range i.e. <200 then check for continuity between the metal of the bridge/strings and the outer case of your jack socket. there should be no resistance i.e. 0 ohms this means a common Ground (Earth) if this is the case then you may have to strip the control cover or scratch plate off to get to the rest of the insides.
If the bridge ground is good, then my next step would be to check the pickup cavities for screaning(sheilding) you will need to take the Pups out and see what type of material is protecting them. If there is non or it is conductive paint I would get some copper or aluminium adhesive backed tape and completely cover the cavities. (I personally then run a wire from the screen to the case of one of the Pots or in my case a common Ground stud which connects all of the grounds together) this way all of your returns have the same or common ground.
I hope this helps. If it is non of these it may be the location you are using your equipment, I know flourescent tubes, light dimmers, electric motors, all to create noise or hum to some extent this can also be transfered through your mains power supply.