I have some notes to share. I had tested the common HC-05 bluetooth module for a datalogger. As far as transmission goes, at 9600 baud, the transmitter stayed on for 5 seconds and in those 5 seconds consumed 20mA. Idle current was around 2mA average. Obviously if you use a FET to turn on/off the bluetooth module, it will go down to nil, just give the BT link enough time to reestablish itself. You can set it to do so automatically by pairing them internally. For the HC05/06, this was done with AT+command.