Grainger, I remember (now that you remind me...) the battery bias on drivers - works like LEds in that the bias is fixed. The battery is on trickle charge from the cathode current, so it's important to understand the battery's limitations!
For the 2A3 however, the fixed bias voltage is a problem as the tube ages - it will change the current too much for consistent operation. That's the real reason for using a resistor, it's self-compensating.
The capacitance should have a low impedance relative to the intrinsic cathode impedance which is 1/gm; this should be the case at some low frequency - I use 5Hz unless I need to cut it close. That works out to
C = gm/(2*pi*f)
or, at 5Hz, C = gm/31.4
That's 159 uF if gm is 0.005 mA/v (5000 micromhos). It's 40uF at 20Hz (the resonance of the plate choke/parafeed capacitor in Stereomour) which is at least an arguably good point to choose. I used 47uF in Paramount.