In the past, I created a Self Service policy with Files and Processes payload. For Execute Command at the bottom, I entered:

open /System/Library/CoreServices/Menu Extras/Bluetooth.menu

This would work on 10.15 and down. But in Big Sur, I don't see it in the CoreServices part. Interested to see if anyone else has a better script. I found this but didn't test it...

https://stackoverflow.com/questions/61594368/show-bluetooth-volume-in-menu-bar-apple-script

Unfortunately Big Sur does not have /System/Library/CoreServices/Menu Extras/Bluetooth.menu”
When I turn off BT using the GUI it writes to these plists.
defaults write com.apple.controlcenter "NSStatusItem Visible Bluetooth" -bool false
defaults write ~/Library/Preferences/ByHost/com.apple.controlcenter Bluetooth 24
But modifying those plists from the command line does not seem to force the change.

These two commands will take effect immediately even in Big Sur: