On July 25, 1896, Broderick was ordained a priest for the Diocese of Hartford by then Bishop Francesco di Paola Cassetta, who was the Patriarch of Jerusalem and Viceregent of Rome. Broderick returned to the diocese and was assigned as a pastor in West Hartford, Connecticut. From 1898 to 1900, he was a faculty member at St. Thomas Seminary at Hartford, Connecticut. When his former Italian instructor, Bishop Donato Sbarretti, was appointed as the ordinary of the Archdiocese of San Cristóbal de la Habana, he appointed Broderick as his secretary. On June 25, 1900, Broderick became the administrator of St. Francis de Sales Church in Cuba. He would later become the administrator of San Carlos and San Ambrosio Seminary. On May 20, 1902, Broderick represented the Catholic Church recognizing the establishment of the Republic of Cuba. While in Cuba, Broderick had to settle claims against the United States government because of damage done to church property during the Spanish–American War. There were rumors his brother was involved with a government contract to install a sewer system in Havana. Bonaventure Broderick sued his brother, David A. Broderick, in a Hartford, Connecticut superior court over some Cuba contracts and won a judgment. It was unclear why his superiors were angry with Broderick.
Episcopacy
On September 7, 1903, Broderick was appointed as the Auxiliary Bishop of the Archdiocese of San Cristóbal de la Habana and Titular Bishop of Iuliopolis. On October 28, 1903 he was consecrated as the Auxiliary Bishop of San Cristóbal de la Habana. His Principal Consecrator was Archbishop Placide Louis Chapelle with Archbishop Francisco de Paula Barnada y Aguilar as the Principal Co-Consecrator.
Resignation
On March 1, 1905, Broderick resigned as Auxiliary Bishop due to a misunderstanding with Pope Pius X and the Vatican over the collection of some funds.
Restoration to episcopal life
While doing some archdiocesan business in Millbrook, New York, New York Archbishop Francis Spellman found Broderick running a gas station in Millbrook where he also wrote a weekly column for a local newspaper. In November 1939, the Vatican asked Spellman to rehabilitate Broderick and Spellman complied. Broderick resumed his public role as a bishop and was made a chaplain of a hospital in Riverdale, New York.