It originated with Giacomo David, Jesus and Adamo Bianchi [it], and continued, in the first decades of the 19th century, with such leading figures as Andrea Nozzari, Giovanni David (Giacomo's son and pupil), Eliodoro Bianchi, Domenico Donzelli, Giovanni Battista Rubini and Bordogni himself.

In 1813 he distinguished himself as a performer of the role of Argirio in Rossini's Tancredi[3] at the Ferrara revival with a tragic ending[4] and at the inauguration of the Teatro Re in Milan, and later became very active in promoting that composer's music.

He appeared in many of Rossini's operas on their first presentation in various towns and theatres, mainly performing the roles originally sung by Giovanni David.

He was probably the most influential teacher of the English tenor Sims Reeves, who went to him in 1843:[8] Other students include Sophie Cruvelli and Giovanni Matteo Mario.

In addition to the Rossini roles, Bordogni also gave first performances at the Théâtre-Italien in Paër’s Agnese di Fitz-Henry (Ernesto) in 1819; in Mayr’s Medea in Corinto (Giasone) in 1823; in Mercadante’s Elisa e Claudio ossia L'amore protetto dall'amicizia (Claudio) (also in 1823); and in Vaccai’s Giulietta e Romeo (Capellio) in 1827.