In 1832 Bagioli was appointed "gran maestro" (or conductor, or musical director) of the Italian opera company of Giacomo Montresor, a French tenor. This company was the first (or second) Italian opera company to visit the United States, and Bagioli traveled to New York City with the company. There, Bagioli called on Lorenzo Da Ponte, the noted music teacher. He had worked as Mozart's librettist on such works as "The Marriage of Figaro" and held the chair of Italian Literature at Columbia College (later Columbia University). Da Ponte's son, also named Lorenzo and sometimes called Lorenzo the Younger, was a professor at New York University. There, Bagioli met Maria (or Eliza) Cooke (1819–1894). She was the adopted daughter of Lorenzo Da Ponte and said to have his "natural" child. (He would have been about 70 when he fathered her.) Maria was from Croton Falls, in Westchester County, New York.