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Do NOT run them in series. Remeber that voltage drops in series add. By running them in parallel, you'll keep the same voltage across the player and the bluetooth transmitter. The only thing this does is increase the current draw on the battery. Naturally, this will decrease the time your battery will lasts, but I suspect that the bluetooth transmitter does not have a very high current draw at all, so it shouldn't be much of a problem at all.
This sounds like a fantastic idea. Best of luck.
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