Quality of amps in bridged mono ?

It will change. I am not sure, but if I remember correctly either the slew rate or the damping factor changes by a factor of 2. If you run a search you will probably find the answer.

Amps can apparently be bridged in parallel or series.
This will make a difference in results......but not the fact that generally things go.....downhill.
Some, my old Rotel RB-1070, for example didn't even spec 4ohm stereo power and only listed 8 ohm bridged....apparently no 4ohm loads allowed in bridged mode.
Of course, a speaker with 8ohm 'nominal' can have some severe dips, so you really must be careful.

Running Bel Canto 200.2's in bridged mono driving Martin Logan SL3's. They are phenomenal.

In bridge mode output voltage is doubled and the power is quadrupled - therefore each of the amps delivers twice more power. Power supplies are not likely to be designed for 200%. Damping factor will drop by a factor of 2. Slew rate should be 2x but output has to deliver twice current and might get slower. I would guess it will stay the same.