How to bi-amp with 2 two-channel amps?

Probably one amp for highs and the other for lows (vertical bi-amping) is best, but, depending on what amps these are, that may not be the case.

A lot of 2 channel amps dont perform well when they are bridged. i.e. one amp for the left speaker and one for the right (horizontal bi-amping).

This is just my opinion of course, others will probably vary.

With 2 identical amps, I'd personally dedicate one amp to the left channel, and one amp to the right channel.

Dedicating one amp to each channel does not consititue as "bridging." Bridging is when you have the ability to combine multiple channels into a lower number of channels (i.e. a 2 channel amp into a 1 channel amp, or a 6 channel amp into a 3 channel amp).

You can do it either way but here is my suggestion and the reasoning behind it.
Use one amp on each speaker. One channel drives the highs(and/or mids) and the other drives the lower end. The reason I feel that doing this is better has to do with the power supply only having to supply higher current to one channel of each amp. It allows the amp to work easier. One channel isn't drawing much from the supply(highs) so the other side can use the extra draw. It allows the amp to drive the lower side a little better(generally cleaner).
The one caveat is both channels need to be reasonably close in input sensitivity to allow your speakers to remain balanced in the frequecy spectrum.
You can use "Y" connectors at each amp or simply solder a wire across the hot leads on the inputs of the amp from left channel to right channel.
Y connectors will degrade your incoming signal a touch.

Horizontal bi-amping allows you to use two different types of amps ( i.e. tubes for highs, SS for bass) you can also use two identical amps. When horizontal is choosen you will use one amp for right and left channel upper and the second amp for right and left channel lower. Note when using two different amps that the gain be the same or an imbalance will occur.Vertical bi-amping uses two of the same type of amps being eiter SS or Tubes. When using vertical bi-amp each one of the amps are dedicated to each speaker, for instace, the left channel of each amp connects to the lows and the right channel connects to the highs.If your preamp doesn't have dual pre outs then you must use a Y connector or spliter. There are a few companies that sell the adaptors.