Assuming it is "unix:path=/run/user/1000/bus", what would be the command to start Firefox as the normaluser with that setting?
DBUS_SESSION_BUS_ADDRESS=unix:path=/run/user/1000/bus \
DISPLAY=:1 \
sudo -H -u normaluser \
--preserve-env=DBUS_SESSION_BUS_ADDRESS,DISPLAY \
firefox
I'd add -H to the options of sudo to make it set the home to normaluser's one.I assumed that your DISPLAY is :1, which is what my Debian has set for me. That's another variable that you could read from the environment of Firefox.
You might have to pass/preserve other environment variables to make Firefox work.
(You could also test the extreme case: Just copy all the env vars.)