Why would you leave it on if you are not using it? No, leave it off. It will drain your battery if on. Anytime you have another radio on you use more battery.
EVO-LUTION 3D
I use the free Juice Defender app in market place, to automatically turn on my bluetooth when I connect it to a power source (Car kit) and then automatically turn it off after 1 minute of it not being connected to anything. Super Convienent!!