These are not the same thing. I am quoting and adding from another thread which put it simply:
Bi-amping requires a speaker with two sets of speaker terminals, one for high, the other for lows. Each terminal set is run to a separate power amp. If you do not use a powered crossover before the power amps, it's called "passive" biamping and all amps should have the same gain. However as many times one does this with the goal of eliminating the negative effects of a passive crossover, the purpose may be defeated.
The disadvantage of bi-amping is mainly cost because you need more amps and an electronic crossover. You have to either have speakers that are made to be bi-amped or you must modify them (remove the crossover and add a second set of speaker terminals). And there is a lot of work to set up the system to make it play correctly. Bi-amping is not plug and play. You need to set the crossover frequency, set the gain for each speaker's driver, and set the time alignment for each driver, too. Otherwise, just don't do it.
Bridging is when two channels of a stereo amp that's made to allow for bridging are combined into one more powerful channel. The down side is that this bridged amp "sees" the speaker load as one half it's rated nominal impedance so it works harder. Another thing to keep in mind is that not all stereo amps are made to be bridged. You can blow your amps etc. if this is not carefully managed.
Honestly, in your case, I would not recommend either bridging or bi-amping. Often you are much better off with a good new 2 channel amp with more power (if that is what you need).
Hope this helps.