Well, if you're rectifying 18 volts with a bridge rectifier and a capacitor, I can tell you that you're getting around 24 volts out. To get that down to 6 volts, you have to drop 18 volts. All of that current goes directly into heating up the linear regulator, that's 4.5 watts. That math is certainly not suspect.
I have the exact same linear supply that was first mentioned here, and my test confirmed that it does indeed get plenty hot with a 1/4 amp load powered by 16 volts AC from a 1033 transformer. All of that heat was in the regulator, and yes it has a reasonable heatsink on it.
I'm not sure what you're looking for here, but the computations and empirical tests agree on the heat issue. I've computed it and I've tested it, and the results are the same.
You said:
A standard Constant Voltage regulator has a very small ground current. While the input wattage to the Full bridge is as stated, the Regulator shouldn't be seeing that power, nor that poor of an efficiency?
This is where you're going wrong, linear regulators have very poor efficiency when the input/output voltage ratio is significant. If the input voltage is closer to the output voltage, you dissipate far less power, that's not the case here.