Here's what I'm suspecting is happening...
Depending on the order scripts are running, you're instantiating a bullet after the shoot command has already been dealt with. Then, when the time for the next shot is available, the stagnant bullet is still ready to accept the next Shoot() method. So, then the next bullet.
You may want to debug those processes.
I'm still not totally secure on the OnEnable/OnDisable parts of the new system, but I believe bulletControls.Disable() will turn off the receiver for the button presses.
...Now that I'm reading it again. I think this is the long winded explanation to. "Yeah, what Max Frymark said."