I am trying to use AirPlay mirroring in a conference room-style setup using a 3rd-generation Apple TV. All software is fully-updated (as of 7/24/2014).
All devices are connected to a strong network without any password.
From an iPhone 4s, the AirPlay service shows up in control center, and mirroring works fine. From an Early 2014 MacBook Air, AirPlay never becomes available in the menu bar or in Display preferences, OR in regular iTunes.
What should I do to try to troubleshoot this?
EDIT:
I had been wondering if there was a subnet issue of some kind, but it appears not. For illustrative purposes, the Apple TV is 10.10.17.217. Two iOS devices can AirPlay to it from .18.8 and .18.196, but the MacBook Air cannot from .20.127. All have the same subnet mask of 255.255.240.0, and are pointed at the same router (.16.1).
I suppose I still need to try with other AirPlay endpoints and with other MacBooks, but I've really got nothing to go on beyond guess and check.
Aaaand I just checked with an iMac connected to the same network, .17.118. Nothing.
...
OKAY HOLD ON A SECOND.
I did a teeny bit of Googling and found some references to Bluetooth being added as a substitute/supplement for Bonjour discovery of AirPlay in a recent update. On the hunch that iOS devices are a bit more promiscuous with Bluetooth than the Macs would be, I tried testing the iOS devices with Bluetooth turned off. Here's the thing: once you're connected, you can turn off Bluetooth, but if Bluetooth is not turned on, you will not be able to see the AirPlay endpoint.
I noticed there was a Bluetooth setting in the Apple TV as well, and saw that it was just on and searching. Upon turning it off, the AirPlay option immediately disappeared from the iOS devices. Back on, and the option reappeared. Still nothing from the Macs.
The Apple TV is running software version 6.2 (6698.99.50.31).
What the hell is going on here?