The bishop beam is a deleted Forerunner weapon in Halo 4, present in the map files. It is a directed energy weapon which functions much like the Sentinel beam. The file for this weapon can be found in the level Shutdown.
As the Promethean Watcher was initially called the "Bishop" during Halo 4's development, it is possible that the Bishop beam was its weapon of choice, much like the Aggressor Sentinel's use of the Sentinel beam in previous games. In the release version, the Watcher only makes use of the Boltshot.