First: check content of the following environment variables:
echo $XDG_CURRENT_DESKTOP
>BunsenLabs
echo $DESKTOP_SESSION
>bunsenlabs
In $HOME/.config/variety/scripts/set_wallpaper:
Find the line SIMPLE_VMS, which initially looks something like this:
SIMPLE_WMS=("bspwm" "dwm" "herbstluftwm" "i3" "i3-with-shmlog" "jwm" "openbox" "qtile" "xmonad")
Add “BunsenLabs” / “bunsenlabs”, like this:
SIMPLE_WMS=("bspwm" "dwm" "herbstluftwm" "i3" "i3-with-shmlog" "jwm" "openbox" "qtile" "xmonad" "BunsenLabs" "bunsenlabs")
Save, and restart variety.