He was raised to the rank of honorary chamberlain of his holiness on 15 March 1923, and appointed Secretary of Briefs to Princes in 1931.

He attended the Second Vatican Council from 1962 to 1965, and participated in the 1963 papal conclave that elected Pope Paul VI.

One of the Vatican's leading Latin experts, Bacci strongly opposed the introduction of the vernacular into the Mass.

[3] In what was known as the Ottaviani Intervention, the 84-year-old Bacci, together with 79-year-old Alfredo Ottaviani, sent to Pope Paul VI, with a short covering letter from themselves, a study by a group of theologians under the direction of Archbishop Marcel Lefebvre criticizing the draft Order of Mass of the revision of the Roman Missal.

Among Bacci's publications was Lexicon Eorum Vocabulorum Quae Difficilius Latine Redduntur, a dictionary of modern terms in Latin; he invented such words as gummis salivaria ("chewing gum"), barbara saltatio ("the twist"), and diurnarius scriptor ("newspaper reporter").