When bridging a AVA solid state amp you are summing the voltages of each channel, i.e. doubling the output voltage. Power varies with the square of the voltage. That means, theorectically, 4 times the power. However, the power supply runs out of electrons before that.
The load is shared equally by all the output mosfets and the heat is shared by the heat sink. The left and right channels are not really working any harder than they would unbridged, they are just working together.
I hope this helps.
Regards,
Dean