I got it to work. It is very simple to do. Here is what I used (although I am positive that these aren't the only choices to get it to work).
• Aukey BR-C1 Bluetooth audio receiver. (got it on amazon for $10)
• Fiio Headphone amp (FiiO A3 E11K)
• Wired Headphones
Once you have charged the first two devices, go into the apple tv's settings --> remotes & devices --> bluetooth. Follow the instructions included with the bluetooth receiver to pair it to your apple tv.
Once this is done plug a 3.5mm audio cable from the bluetooth reciever, into the input on the headphone amp. Plug your headphones into the headphone jack. Everything should be working. Adjust the audio setting on the headphone amp and enjoy.
Again, I am positive there are many other hardware options that could work. All you need is a bluetooth audio receiver and something to amplify the sound coming out of it.
Good Luck!
Just an FYI, my purpose in doing this is to be able to use it when I travel for work. I am on the road 60+ nights a year for work. I can hook this up to hotel TVs, stream plex from my home network, and crank up the volume without annoying people in other rooms. This would also work as a midnight mode so you don't wake other people.