What are your results after having the Gear Live for a full day? Also include the phone you are pairing it with.
Bluetooth is bluetooth, if you have the latest version of bluetooth sure the bluetooth uses a bit of the battery but having the phone talk to your watch, bluetooth headset or car makes no difference.
The watch no sooner affect your battery life than any other bluetooth device will.
I never turn bluetooth off, hop in car the phone pairs with the car, go for a jog pairs with the headphones.