Please provide all makes/models of hardware involved so we can assess properly
In general I would dissuade you from going with bluetooth since the sound quality is poor and other better options are usually viable.
I have a room set up with multiple DirecTV receivers (3) and TVs (also 3). One is going to surround sound, looking for options/ideas so others can get audio from other tvs. Can multiple Bluetooth setups be an option, is that even possible?