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Bluetooth modules don't use a lot of energy so it's ok to use these. The good thing about it is that it's small. One drawback is that you would have to step up the voltage to 5V to use it with the isolator.
A cheap way to solve this is using a DC/DC isolator between the battery and the Bluetooth module. Just search for "dc/dc 0505 isolator". But notice that there are 1 watt and 2 Watt Models. Depending on situation, 1W can make the Bluetooth modules integrated "preamp" distort when a lot of bass is transmitted from your source to the module. I have also seen that people solve this by adding one buffering capacitor parallel to input and a second one to output of the dc/dc isolator.