Not all amps can be bridged. Even so, those that CAN be bridged are usually at 4 ohms TOTAL bridged. That seems to be about the industry standard unless you get a more powerful, competition-based amp. You can either wire subs in a parallel or series configuration. I'm guessing you did a parallel wiring scheme, to bring the resistance so low.
As you said, the amp can push 100x2 at two ohms. That means EACH channel can push 100 watts at 2 ohms. *Or bridged, 4 ohms total, because both channels are pushing 2 ohms to meet the 4 ohms bridged.* You most likely needed to get subs that will have the right resistance to meet the 4 ohm spec, which would be dual voice coils subs that could each create an 8 ohm load. Then after you bridge them in a parallel config, it would yield a total of 4 ohms bridged, making each channel of your amp push at the correct 2 ohms EACH.
I think what happened in your case is that you paralleled two 4 ohm subs, which then makes a TOTAL of 2 ohms. However, in the bridged config to meet this power demand, each channel is pushing 1 ohm EACH to create a total of 2 ohms bridged, which is too much for most amps.
You won't really be able to bridge the amp with two 4 ohm speakers to get more power. You'll need to just put each speaker to a channel and pull four ohms. Your other options are:
1. Buy two more 4 ohm speakers to start messing around with the ohm loads correctly.
2. Junk the current subs and buy two dual-voice coil subs that will get you the desired loads of 2 (series) or 8 (parallel)ohms to bridge the amp to the desired 4 ohms.
Sorry this is so involved, but ohms calculation takes more than a small post.
