In layman's terms, what is the theory on why bootstrapping adds more gain?
Sometimes it helps to plug in some numbers (and sometimes it doesn't). Referring to Valve Wizard's drawing, let's say we have a 10V change at the plate of V1. Without bootstrapping it would take a change of 10V / 94K = 106uA to get the 10V change at the plate (Ohm's law).
Now let's say that a 10V change at the plate of V1 causes a 9.5V change at the cathode of V2. This 9.5V change is coupled to the junction of R1 and R2 by C1, so that end of R2 has a change of 9.5V. One end of R2 has a 10V change and the other end has a 9.5V change, both changes are in the same direction, so there is a change of 0.5V across R2. 0.5V / 47K = 10.6uA change. Already we are getting a sense of increased gain because it only takes 10.6uA to get a 10V change with bootstrapping whereas it took 106uA without bootstrapping.
By Ohm's law, 10V / 10.6uA = 940K. So R2 appears to be 940K to the plate of V1 with bootstrapping. Say the mu of V1 is 100 and the internal plate resistance is 60K. A voltage divider is formed by the 940K and the 60K. When mu is spread across this voltage divider, most of it is across the 940K. If the cathode were fully bypassed, the gain would be mu times the voltage divider: 100 x (940K / 1000K) = 94.
This explanation is subject to peer review.