Rooney scored three and Javier Hernandez bagged a brace on his first start of the season as United responded in style to rivals City's 3-0 win over Wigan earlier in the day.
Rooney told ESPN: "We always know Bolton is a difficult place to come.
"We got an early goal and kicked on from there and it could have been more.
"First start with Chicharito (this season) and both scoring, that's great."
He added: "I had a long time to rest and get a good pre-season under my belt. I've stayed free of injuries and it's helped me for the start of the season."
Hernandez missed several chances to complete a hat-trick of his own, but said: "The most important thing here is the result. We get three points from a difficult visit like Bolton."
On his partnership with Rooney, he added: "Every player can play with Wayne Rooney. He's a world-class player. He can do anything."
The win ensured United did not allow City to steal a march on them with their earlier win.
United boss Sir Alex Ferguson said: "You just have to concentrate on yourselves. It's a difficult start to the season, we've got all the bigger names. We've got Chelsea next Sunday.
"It's a hectic start and if we come through it, well have done well."