It was a comfortable afternoon for the hosts as they took the lead in the first-half through Sergio Agüero. However, Eddie Howe's side were able to hold their own for the majority of the half and were perhaps slightly unlucky to find themselves behind at half-time.
However, the second-half was a different story as Raheem Sterling doubled City's advantage early on which allowed them to take control of the game. A second goal from Agüero made sure of the three points before Danilo added gloss to the scoreline late on.
Guardiola was delighted with how his players have responded to a challenging number of fixtures in a short period of time.
He said: “Always you have doubts after a lot of games in a row. Mentally were we ready to do it again and again? That is what impressed me the most about the guys. Every time they are ready to adapt and of course it is not easy."
He added: "Bournemouth (played) a high line so it was not easy to find space between the lines. We make a good first goal and the second one helped us a lot to be more controlled. In the last 15 to 20 minutes, we found our tempo and space and we scored four beautiful goals."
Is Agüero City's main striker?
Guardiola has two superb striking options to choose from in the form of Agüero and Gabriel Jesus and the debate about which player is better suited to City's style of play continues to rumble on. Agüero certainly did not do himself any harm in this match as he scored another two goals with his first being his 100th strike for City at the Etihad Stadium in all competitions.
Guardiola says he understands Agüero's frustration when he is not selected but believes he has many players who deserve more of a chance than they are currently getting.
He said: "I was a football player, I understand that when they are substituted or do not play, they are sad. I try to have the best relationship as possible with my players. I sometimes think that Gabriel (Jesus) deserves to play too."
He added: "The important thing is they respect between each other. They can be (unhappy) with me, that is not a problem. They have an amazing relationship between them. It is a dream every day to go and train with them."
Despite speculation that he has a frosty relationship with Agüero, Guardiola stated that he has "a lot" of respect for the striker and that he is so "happy to have him" at the club along with Jesus.
Is Sterling in the form of his life?
The 23-year-old winger has played a key role in City's storming start to the season and scored his 12th goal of the campaign against the Cherries. Guardiola believes he has improved significantly since he arrived at the club and is now reaping the benefits of his hard work.
He said: "With and without the ball, he is so aggressive and intense. He knows exactly when he has to dribble and when he has to pass the ball. Now he is enjoying scoring goals. He is amazing on the counterattack and is loved in the dressing room."
He added: "He is an important player for the international team. The most difficult thing for football players (of that) age is to maintain every single game that level. He is doing that."
Next up for City is a trip to St James' Park on Boxing Day to face Newcastle United. Guardiola will be hoping that his side can continue their incredible run by claiming another three points.