He was born in San Giorgio La Montagna, now known as San Giorgio del Sannio. His father was Ciriaco Bocchini, a wealthy landowner, and his mother was Concetta Padiglione, a member of the aristocratic but liberal Padiglione family. Bocchini studied Law in Naples and then joined the Police as an officer. After Mussolini took power in 1922, Bocchini was appointed Prefect of Brescia (1922–1923), then Bologna (1923–1925), and finally Genoa (1925–1926). In 1926 Mussolini made Bocchini Chief of Police following the advice of Luigi Federzoni, who knew him from Bologna. Bocchini had control over the regular Polizia di Stato and also over the OVRA, the political police of the Fascist Party; however, the Carabinieri remained outside his grip, and were influenced to a significant degree by the King.
Bocchini went on to arrest many prominent anti-fascists, including Antonio Gramsci. He died in November 1940, after suffering a stroke.