Born in Brescia, Bonetti made his debut for his hometown club, Brescia (1981–84), before moving to Serie B side Genoa (1984–85), and subsequently defending European Champions Juventus (1985–88), where he won the 1985 Intercontinental Cup, and the 1985–86 Serie A title; he made his Serie A debut on 10 November 1985, coming on as a late substitute in a 3–1 home win over Roma, the club for which his brother Dario was playing at the time. During Ivano's time at the Turin club, he was also sent on loan to Atalanta for the 1987–88 Serie B season, helping the club to obtain a fourth-place finish and Serie A promotion. He later played for Bologna (1988–90), and Sampdoria (1990–93), where he won his second Serie A title in 1991, also reaching the European Cup final the following year, playing alongside his brother Dario once again. He later returned to Bologna (1993–94) in Serie C1, before briefly returning to Brescia the following season (1994–95), and spending the second half of the 1994–95 Serie A season with Torino, before moving to England later in 1995.