Born in Milan, Bolchi made his debut at the age of 18 with Internazionale in a Serie A away match lost 1–0 to Napoli on 18 May 1958.

[1] He captained the side between 1961 and 1962 and obtained notable success during his spell with the club, winning the Serie A title in 1963, and the European Cup in 1964.

He first coached a Serie A team, Cesena, in 1982, but did not manage to save it from relegation.

On 23 April 2007, with just five matches remaining before the end of the league, Bolchi was appointed head coach of Messina, a team he already coached in their 1975–76 Serie C campaign and, for six matches, at the end of the 2002–03 season, in Serie B.

He did not manage to avoid relegation, also due to Messina's poor league table well before his appointment, and finally retired from football after the end of the season.