The woman, who did not want to be named, said the bus was full and one of its passengers was pregnant.
Disappointed tourists were also on board.
The bus left Auckland at 7.15am, and was originally due in New Plymouth at 2pm after passing through Waitomo at 11am.
Its replacement is not expected to arrive in New Plymouth until about 9.30pm.
Naked Bus managing director Hamish Nuttall confirmed the six-hour delay. He said replacement buses were sent as soon as the company became aware of the mechanical problems.
He said he was very sorry for the inconvenience and the company would be refunding passenger fares.