I would not bi-amp personally unless using a crossover before the power amps but that's just me. There are theoretical advantages of bi-amping without a crossover but in practice the difference is negligible in all but pathological cases (prepare to hear some, I am sure).
Bi-wiring simply moves the shorting connection on your speaker to the amplifier. The speaker wires can thus act like a filter, assuming the amplifier has low output impedance (high damping factor), again for a pathological case were the speaker load is very low impedance and speaker wires are high enough in resistance (impedance) to provide isolation. If that is the case, you need larger speaker wires, unless you really want your speaker wires acting like filters...
Chances are all that was too technical but I'll muddle ahead about bridging. Given two amplifier channels, normally they operate independently, say one left and one right channel, with voltage gain G, both referenced to ground (0 V):
Vout(L) = G * Vin(L) = G * [Vin(L) - 0]
Vout(R) = G * Vin(R) = G * [Vin(R) - 0]
You connect your speaker from the Vout(L/R) positive (+) terminals to ground (0). The gain simply means you've increased (multiplied) the input voltage by some amount (G) to produce a higher output voltage -- that's what amplifiers do.
Now bridging takes a single input and applies it to both amplifiers, inverting one amplifier to double the voltage swing (multiply by -1):
Vout(L) = G * Vin
Vout(R) = G * Vin * (-1) = G * (-Vin)
I left off the 0 V reference. Now, instead of taking each output with respect to ground, you take the output across the two (+) output terminals. The inversion means you are subtracting a negative number and so you get a positive result:
Vout(L-R) = G * [Vin - (-Vin)] = G * [Vin + Vin] = G * 2Vin.
OK, so bridging ideally doubles the voltage swing. You can think of it like putting the two amplifiers (voltage sources) in series (not really right but hopefully you get the idea).
Now, power goes as voltage squared:
Power (watts) = Voltage (V) * Voltage / R where R is the impedance of your speakers in ohms.
Since bridging doubles the voltage, and the square of 2 is 4 (2*2 = 4), ideally it quadruples the power output. A 50 W/channel amplifier should ideally produce 200 W when bridged. In practice there are other limitations (power supply capacity, thermal/heat dissipation, and so forth) so bridged amplifiers are usually specified at around 2x to 3x instead of all the way to 4x the non-bridged power output. Still get reasonable power increase.
There are catches, of course, like typically
higher noise and distortion, and greater load sensitivity. The latter means that, in bridged mode, an amplifier is typically at twice the load impedance. An amp rated to drive 4 ohms/ch will probably be rated to drive 8 ohms minimum when bridged. Twice the voltage also means twice the current, and amps are not usually rated for that much current without overheating and such. (That is partly why the bridged power rating is usually not fully 4x the normal rating.)
HTH - Don