If you want to make a cold biased Class-AB amp, cathode bias isn't a good place to start. You would use fixed bias, though nowadays you can cheat by putting a Zener diode in parallel with the cathode resistor. However, cold bias tends to sound pretty bad for guitar.
With hot bias, it works reasonably well. The voltage across the cathode resistor just increases a bit as the amp is driven beyond its Class-A region of operation.