Bluetooth is not speedy enough for almost all screen work. But it can be done. Maybe you were searching for a ready to use solution. One could create such a link but you would be writing code and more since you wanted to do this over Bluetooth.

As to the 4.6 to 4.7 screen I never found that size. 4 inch Android devices are plentiful so maybe there's some Android phone with the exact size you want. Now you have your phone and the screen on the 4.x inch Android. At this point you write your code.