A bypass capacitor implies that it's bypassing a larger capacitor.
The capacitor across the cathode resistor is there to act as a short for AC on the filament, removing degenerative feedback that would otherwise be there.
The cathode bypass cap also stabilizes the bias point, though this becomes unnecessary with the PJCSS upgrade IMO.
The size of the cathode bypass cap must be sufficient to offer the same "short" across all audio frequencies and then some. The 1000uF cap we put in the last Quickie was used because we already had it, the new Quickie uses a 150uF capacitor that we added to our inventory for the BeePre.
-PB