I have a Zenith like this. and I did this when I replaced the selenium rectifier.
Full wave rectification, less power supply hum (120Hz vs 60Hz). The heater string runs directly off the powerline (via power switch). The mid point of the heater string will look to have minimal AC waveform in reference to the B- line of the bridge rectifier. But will have a DC bias of about half the B+ voltage. This is fine, cathodes like their heaters to have a positive bias. One end of the audio output tube (for example a 50C5) (#8 in the diagram) heater is probably already connected to one of the AC lines. Disconnect the heater line of the other audio output heater pin. This line, now disconnected (feeding to tube #7), now will be connected to the other AC line. See diagram. And at the old ground end of the heater string, usually the AM or FM detector/ audio driver tube (#1) (19T8 for example) disconnect from ground and connect to the now loose end of the audio output tube heater. This should minimize hum pickup from the heater line. A small cap of around 0.1uF 400V or more tied close to the heater string midpoint should help reduce the AC waveform some more by holding a bias charge between the heater string and the B- ground of the radio during the time the bridge rectifier isn't conducting. The bridge diodes only conduct at the peaks of the AC powerline waveform.
Pay special attention to the AC line lead dress around the volume control power switch for hum pickup. Hot chassis radios usually switched the local ground feed line to avoid hum pickup from 120VAC to local ground wires. This could ruin the advantage of full wave rectification (less hum, 120Hz vs 60Hz) if not taken care of. Look for trouble by listening to silent passages in radio programming with the volume control at half setting (hum pickup can be more severe at this position). Shielding may be needed.