Bluetooth pairing Apple TV with MacBook Pro

only think bluetoothwise the appletv support is keyboard

and even if it did then bluetooth don't provide enough bandwidth to stream movies

I have the same problem. Twice, almost freakishly, after dozens of attempts, there was a window that popped up saying the Apple TV accepted the pairing, and it displayed the same acceptance code as my MacBook Pro, so I immediately clicked on "Pair." Unfortunately, it failed to pair either time, and I was sent back to my original level of frustration. Perhaps it is that my Apple TV is one of the earlier models. However, it LOOKS like it should pair, but it never lists the MacBook Pro as a Device. It will list the Bluetooth keyboard, but not the MacBook Pro. Frustrating!

APPLE SUPPORT: DO YOU HAVE ANY ANSWERS FOR US?!?

Think Rudegar is correct - AppleTV talks to your MacBook via WiFi, not Bluetooth because of bandwidth requirements for video vs audio. Bluetooth on the AppleTV would be used to pair a bluetooth keyboard or perhaps a Bluetooth speaker.

If you want to share media on your MacBook (like photos or movies) you would do that thru iTunes on the MacBook (enable Home Sharing via the iTunes menu command File/"Home Sharing") and then on the AppleTV you connect to the MacBook using the "Computers" app. You need to establish a common AppleID that they both will make use of as well.

For some detailed comments about how to do this see the http://www.macworld.co.uk/how-to/apple/how-set-up-2015-apple-tv-4th-gen-apple-tv -restart-update-screenshot-record-tips-3630520/

Good luck...

ps - the above link is for the 4th Generation AppleTV (the most recent). The 3rd Generation AppleTV also should work basically the same I think.