Can't charge and use a Li-Po Bluetooth receiver at the same time - can I bypass the battery though?
If you do replace the battery with a USB supply, you should drop the 5 volts down to something closer to 3.7 volts. You could do this with a low drop out 3.5 volt regulator such as the MC33269T  and a small heatsink or you could put two or three 1N400X type diodes in series with the positive lead of the USB supply.