Bonomi was born on 16 December 1536 to a Cremonese patrician family, studied law at the Universities of Bologna and Pavia and received his degree in utroque iure.
Bonomi traveled with Charles Borromeo in 1567 to Ticino and in 1570 to the rest of Switzerland; this visitation is considered to be the beginning of the Catholic Reformation in the Swiss Confederation.
In 1578, at the request of Charles Borromeo, by Pope Gregory XIII Bonomi was sent as a visitor to the Diocese of Como, and he also visited Valtellina and Ticino.
From 27 May 1579 to 16 September 1581 he worked as Apostolic Nuncio with special rights in Switzerland, where he visited parishes and monasteries in the dioceses of Constance, Basel, Chur, Lausanne and Sion and founded the Jesuit College of Saint Michael in Freiburg by Peter Canisius.
His work in Switzerland met with resistance from parts of the clergy and from individual monasteries and from secular authorities, and even the curia repeatedly admonished him to be more lenient.