My cooments are:
The audio connections should be shielded.
it would be Best, if they were shielded at one end only.
Sometimes loops can be broken, if a small resistor like 2.2 ohms is used for the music input ground side.
You really need to post a diagram of your connections and what devices you used.
Loops, generally means if you break the loop, the noise goes away. Breaking what connection causes the noise to disappear?
So, you did say that with two supplies, it works. So, is it possible to use a small isolated switching converter to power the BT module?
The rules are:
Use shielded cable for audio.
The best would be twisted pair shieleded with a differential line driver/receiver, but that won't happen. That like the XLR system for professional audio.
Single return line.
Shields at one end only. If you need the audio return then use a 2.2 ohm resistor to your star point for the audio return.