By default, MPMoviePlayerController enables AirPlay support. If you haven't set it as FALSE. Then, probably you need to check your network or AppleTV's network connection. They need to be in same network (intranet usually).
There is a safe way to detect whether your iOS device is able to find AppleTV. You can double click HOME button, swipe task bar from left to right side, if you can see "Airplay" route button, then you can reach it. Otherwise, you need to check your AppleTV setting to make sure Airplay function is enabled and AppleTV is connected to same network that you iOS device in.
If you are using your own customized video play controller interface, you can embedded the "Airplay" button into your own UI.