Hi,
I am new to retropie, but I was able to run in on raspbian bullseye. I am running rpi4 as a HTPC and audio player. It is not option for me to use pre-made images of retropie as I do not want to install and configure again all services already running on my pi.
So I just gave it a try. I have followed the manual installation steps. First run of retropie_setup.sh ended with errors that quite many deb packages cannot be found or installed. I am not sure why because I could found and install almost all those packages manually using aptitude. Well my system was not fully updated, so maybe that could be the reason.
One more execution of retropie_setup.sh complained about missing omxplayer package. That package is no more part of raspbian but I have succeeded to find it in some raspbian repo: https://archive.raspberrypi.org/debian/pool/main/o/omxplayer/omxplayer_20190723+gitf543a0d-1+bullseye_armhf.deb So I have installed it. I have no idea whether the omxplayer works. What I have read about it, it should not work on bullseye. But retropie_setup.sh was happy with it and compiled the EmulationStation.
Now it is complaining about missing ilclient.hand it cannot build omxiv. Although I have found some sources with the ilclient I even did not give it a try installing them. They wrote it will not work on Bullseye and I even do not know what is the omxiv good for and whether I need it.
Today I was able to run EmulationStation. Well it was quite surprise for me that it works :-). But kids was able to play some old nintendo games, so I am happy :-).