There was minor damage to the side of the bus.
The statement said the occupants ran off and were found by police last night after they were involved in a second crash, in another stolen vehicle.
All occupants have since been referred to youth aid.
Just prior to this incident occupants of a similar vehicle were reported to police as having fired a BB gun or similar on Shirley St, Mangakakahi.
The statement said police were looking to establish whether the incidents were linked.
No one was injured as a result of the crashes or the shooting incident.
Meanwhile, Rotorua Neighbourhood Support has issued an alert to its subscribers to keep an eye out for suspicious activity around vehicles.
The email alert said there had been several Mazda Demos targeted to steal in the past month.
"Please remain aware of groups of youth in and around your business, they are very young, aged around 10 to 17 years old and as they would normally be at school at that age they stand out so it would be appreciated if you could ring 111 if they are behaving suspiciously," the email said.