Arduino Bluetooth Range Control
This should not be the solution to your problem which is btw. not exactly clear. Do you want to prevent people outside of this range to connect, or do you have some sort of interference problem (in this case it might be legitimate)? 

Unauthorized access should not be controlled by range because it depends not only on your sender antenna but also on the gain of the receiving device. Anyways, in the frequency bands and energy levels of a Bluetooth antenna a potentiometer will not work. 

Implement access control beyond the pairing in your application.

There should be some fancy Bluetooth devices that allow for energy control. Especially, low-energy devices.