"While we understand that there are safety issues of just anyone travelling on a school bus, it was important to be on the bus with the kids to see how the dust affects them," Mr Peters said.
"The Ministry informed the organisers at the last minute so we have to question what interference there has been at high levels in the decision-making."
Mr Peters said the Government had failed to take the families' concerns seriously, and the bus ban was a continuation of that position.
"Minister of Education Hekia Parata must provide answers as to today's appalling and disgraceful decision-making."
Kim Shannon, the Ministry of Education's head of the education infrastructure service, said its transport agent had been advised by Ritchies that Mr Peters wanted to travel on the bus.
"Ritchies had health and safety concerns about this. Under the terms of Ritchie's contract, they are not able to carry adults or any other ineligible passengers without our permission."
The bus is a 20-seater vehicle and Ritchies advised that it carried 20 primary and secondary aged students on it.
"Our transport agent advised us that carrying Mr Peters and other adults in his party would placed the company at risk of exceeding the limits of the Certificate of Loading and could mean not all children would get seats," Ms Shannon said.
"As this request was made at such short notice, it wasn't possible to ensure that we could ensure the health and safety of the children on the bus under these circumstances. We informed our agent to turn down the request."
If more notice had been given Mr Peters may have been allowed on the bus, Ms Shannon said.
