Bridging is all about speaker impedance - it doesn't provide any more power, it just provides it to a different impedance. So your TDA2030 amp can provide 10W per channel into 4 ohms, that's a total of 20W into two speakers. If you bridge the two amps, and put the speakers in series, you get exactly the same 20W into the exact same speakers, but now mono instead of stereo.
So it's only useful if you want to provide more power into one speaker of a higher impedance - as Audioguru mentioned, it's main application is to get more power from a low voltage supply.