Thanks Xcamr
you solved my problem as well.
Now I can play late at night and not wake people up
Here the info for anyone with a similar problem :
Go to King's Bounty/data and look for the default.ini file. Open it with notepad and at the end there is a section called , Integer Parameter. the line you want is, setf ~cl_force_soundcard -1
Change that -1 to 1 and then save file and load the game.
Now the bluetooth headphones work when they are on and the speakers work when I am not using the headphones.