This is not what you're hoping for. We use an application on our desktop computers at our school to share ipads to the computers>projectors since all of our projectors are VGA and lack the HDMI for an Apple TV hook.
The applications displays the available computers accessable, which will label as the computer name. It may look like it's bluetooth, but it's not.
Thats what these are for http://store.apple.com/us/product/H9139VC/A/kanex-atv-pro-hdmi-to-vga-adapter-with-audio-support
We have just started deploying Apple TV's, Macs and iPads to our teachers. Loving it. Airplay just gives them so much freedom.