Does RF transmitter transmit all the time?

So what is the simple way to stop transmission and enable it only before I want to transmit something?

Why do you want to?

You could see how much power they draw. If it is less that 20mA, you could power the radio from a digital pin, and turn that pin on and off as the need to transmit data arises/goes away.

There will only be data available to be read when the receiver receives data, so turning the sending radio off won't have any affect on the receiver.