Airplay via bluetooth

I plan to stream views from iPhone 5 app to Macbook pro ( 13" Retina -latest model) through Airplay using Bluetooth connection. Consider that there are no internet connection and cellular data connection. Both devices (iPhone 5 and Pro) are able to see each other and try to Pair but will not connect. I have gone through Forum and Net to see any possible solutions without success.

Shouldn't these devices from Apple connect in a click? I appreciate for any solution.