Feathery Bolshevik Investigations (or FBI for short) is an organisation that helps players to spot hiding penguin spies while playing the Penguin Hide and Seek game which is part of Distractions and Diversions. The organisation helps players by releasing information about penguin disguises.
The name is clearly a play on words referencing the United States criminal investigative agency known as The Federal Bureau of Investigation. Feathery Bolshevik Investigations was created to help spy on the penguin intelligence organisation, the KGP, a play on words with the KGB, a Soviet intelligence agency. In addition, "Bolshevik" was the name of the Communist party during the Russian Revolution.
Because the FBI has only been mentioned once on the Game Guide, it is not known if any RuneScape characters are affiliated with the organisation. However, because Larry is the starting point for Penguin Hide and Seek, it is strongly suspected that he is part of, or in contact with the organisation.