A teenage boy from Green Bay High was admitted to Starship hospital with a foot injury after jumping out.
Mr Sheppard, an associate deputy secretary for education infrastructure service, said Ritchies had undertaken to share its safety and communication procedures with both schools should an incident occur again on any of the company's contracted routes.
That may require the schools to designate a representative to be contactable before and after school, he said in a statement this evening.
Ritchies director Andrew Ritchie defended the driver after the incident as having followed "normal procedure" by not stopping and saying he would take his passengers back to their schools after several were misbehaving.
It is understood the driver became angry by buzzers being pressed repeatedly after he missed a stop near Laingholm.
Mr Ritchie said on Monday he welcomed the police decision not to press charges against the driver and suggested some school bus runs might need extra help in the form of adult supervisors travelling with large numbers of children.
Although the driver was stood down from school bus duties during the police investigation, Mr Sheppard indicated no further action would be taken against him now that the inquiry was complete.
But he said the ministry had taken the incident seriously and would be keeping "a close eye" on routes in the area concerned.
"We are committed to supporting schools and transport providers to work towards providing a quality service for students," he said.
His statement did not address several questions the Herald sent the ministry this afternoon, including what advice the police had offered as a result of their investigation, and what role an adult teacher aide on the bus may have taken.
The Waitemata police said on Monday night that the incident was the result of a combination of factors, but would not detail those.
They said they had provided "feedback" advice to all involved parties.
An administrative assistant at Green Bay High said principal Morag Hutchinson would have nothing to add to the ministry's statement.