Hello Artemis 2015,
I understand you want to AirPlay from your iPhone 6 Plus to your Apple TV over Bluetooth with no Wi-Fi whatsoever.
Wi-Fi is needed for AirPlay, but what is not needed is an existing Wi-Fi network. What you can use is peer-to-peer AirPlay where the devices discover each other over Bluetooth and create an ad-hoc Wi-Fi network for the AirPlay.
Use AirPlay to wirelessly stream content from your iPhone, iPad, or iPod touch - Apple Support
Use peer-to-peer AirPlay
With peer-to-peer AirPlay, your iOS device and Apple TV don't have to be on the same Wi-Fi network.
To use peer-to-peer AirPlay, you need one of these devices with iOS 8 or later:
- iPhone 5 or later
- iPad mini or iPad (4th generation or later)
- iPod touch (5th generation or later)
You can stream content to your Apple TV (3rd generation rev A, model A1469 or later) with software version 7.0 or later. Find out which Apple TV model you have.
Make sure that both devices have Wi-Fi and Bluetooth turned on.
If you want to stream iTunes Store content, you also need an Internet connection.
Take care.
