The game, which took place at the City of Manchester Stadium, ended 4-0 in favor of the team of Josep Guardiola.
For City, goals were scored by Ilkay Gundogan (19th minute), Kevin De Bruyne (31st), Phil Foden (37th).
The defender of the losing team Jefferson Lerma (79th) chalked up an own goal.
The Citizens (six points) lead the Premier League.
Bournemouth (three) are in ninth position.
Earlier, the head coach of Manchester United, Eric ten Hag, commented on the information about the desire of striker Cristiano Ronaldo to leave the club.