Do also refer to https://www.home-assistant.io/integrations/bluetooth/
First, we need to add
-v /run/dbus:/run/dbus:ro
To the Docker parameters (also updated in Home Assistant on Docker)
After that, I installed the "Bluetooth" Integrations, but it insisted that AppAmours was blocking and, and "stop" and "disable" of AppAmours was not sufficient. So I removed it completely.
Now, the configure button on the Bluetooth Integration gives me:
And on the underlying Ubuntu OS:
➜ ~ bluetoothctl [NEW] Controller 74:C6:3B:7C:1E:40 sparrow.mos-eisley.dk [default] Agent registered [bluetooth]#
So that should be sufficient !