I just thought I would share this here, since i just found the little trick after receiving an apple tv for Christmas.
To make the NLS bard app play through the apple tv, or any other airplay device, do the following.
1 Select the book you want to listen to with the ns bard app and position it as desired.
2. Start playback on any airplay capable app, such as music.
3. Select airplay under the music app, or whichever you are playing and choose your desired airplay device.
4. start your book playing on NLS bard app. The music or other audio will stop and th ebook will play through airplay.

Maybe we can all E mail the NLS and ask them to add airplay to the app.