Anything transmitting over a distance is going to suck power - hence the use of sleep, and shutting down the transmitter (and everything else) totally when it's not in use.
You just need an interrupt signal that triggers the ESP (or whatever) to wake up, check to ensure it's a valid detection, and then fire up the transmitter - send the data, then go back to sleep.
You need to be aware that if you're using modules, watch out for ones with permanently powered devices on-board, such as the USB programming interface.