LG VX-8100

I have a bluetooth headset and have my phone's bluetooth setting to 'on'. When I have my headset on, the little bt icon on the phone turns blue. That's fine. When I turn my bt headset off, the icon turns white showing that it is not connected anymore, but the icon is still there. Should I turn my phone's bt setting to 'off' so the icon disappears? Am I draining the phone's battery by leaving the phone's bt setting 'on'? Thanks very much for your advice. Great forum!