What you are asking for is not common for most radios. Not sure why except that it is not legal especially in a commercial vehicle to use a headset with 2 ear cups. This pratice is not safe. You cannot hear emercency vehicles.
Most all bluetooth stereos will stream your phones' media to the radio and thru the speakers and not to a headset. Thats the benefit of Bluetooth connection that you can make a hands free connection and answer the phone. The sound is designed to still designed to play thru speakers
So to solve your problem would be to not use a stereo at all. Stream your music by way of the smart phone to ear buds or a headset. Listen to Pandoria or Iheart or any service that lets your phone stream a more radio station like content.
Note we do have a surface mount radio that is designed to operate without or with speakers and go directly to a bluetooth headset. It is sold on one of our sister sites at HEAVY DUTY RADIOS.com