How to limit any devices to appear on any Bonjour/Airplay capable devices close by? This is an issue at my school district where I work as a network admin. Right now, I could see around the list of at least 15-20 Apple TVs that is located across school buildings when I press on AirPlay function on my iPhone 6. Our only security we have is right now that all Apple TVs require password to access before we can use them. 

What is a good method to limit Apple TVs to only ones that teachers should be seeing in the list to select from? I am trying to find the answer for this on Internet but I cannot find one.
There are a number of ways to do this, depending on your network setup.

You could as @tron_jones suggested use isolated networks or VLANs. Another way would be to setup the router so that each class room is on a different subnet i.e. 

10.0.1.0/24 for class room 1
10.0.2.0/24 for class room 2
10.0.3.0/24 for class room 3

mDNS / Bonjour does not broadcast outside of the subnet by default.

Either of these options should work, but require a non-trivial amount of alteration to your LAN, essentially there is no solution within the product itself.