Unfortunately, there is no such thing for a stock iPhone. You would have to jail break your phone and install something like the tweak SBSettings in order to get that functionality. Sorry.
I'll chime in with why Apple has never added the feature. It isn't needed. Bluetooth in standby mode will use less than 1.5% of the battery in 24 hours. You would waste more power turning it on and off then simply leaving it on due to the screen time alone.