Simulate Battery for Bluetooth Device
Inside the device it likely has a small lithium ion battery that has a nominal voltage of 3.7V. It goes down to 2.8V and charges up to 4.2V. The board likely has a charging IC with some cut off voltage to alert, over charge protection. There is likely only two wires to the battery. 

You could trick it by connecting a regulated 3.5 to 3.7 volt supply instead of the battery And making sure you never connect the usb power supply. Using the usb 5v supply with an adjustable linear regulator like the lm7805 should work. 

This is not guaranteed though.