For MacBook Pro 16" and macOS 10.15.3 all solutions did not work. I did some research and found a way to disable Music. You won't be able to use it afterwards, so only do this if you do not need the Music app.
Since apple introduced some security mechanisms, some things have to be done in advance. At first you need to disable the System Integrity Protection.
Boot in recovery mode [hold + R until apple logo appears]
Login with your user
Open Terminal in Utilities Menu and enter
csrutil disable
reboot [normally]
Afterwards you have to mount your drive with write access because the apple applications are read only. This is non-permanent, after a reboot the changes are discarded.
sudo mount -uw /
Now that the filesystem is writable, you can revoke all rights on Music to prevent it from being opened.
sudo chmod 0 /System/Applications/Music.app/Contents/MacOS/Music
Now, connecting your bluetooth headset won't start the Music app. But you have to turn System Integrity Protection on again:
Boot in recovery mode
Open Terminal in Utilities Menu and enter
csrutil enable
reboot [normally]
You can revert this change simply by giving the system the rights back to read, write, execute the Music App. Remember to turn off System Integrity Protection in advance and mount your drive writeable as stated above.
sudo chmod 755 /System/Applications/Music.app/Contents/MacOS/Music
The Music App should be able to be used again.
Remeber to turn on System Integrity Protection again!