Mr Healey said the company had required the family to complete an unaccompanied minor form, stating who would be dropping her off and collecting her. Tiffany was given a lanyard stating her name and drop-off location.
"Tiffany fell asleep on the bus and the driver failed to wake her up and help her and her luggage off at the bus stop that we had agreed upon with the company.
"When he realised his mistake, he pulled over at the side of the road and kicked her off the bus at around 8.45pm. It's an absolute disgrace.
Never in a million years did we expect her to have to go through this kind of ordeal.
"Anything could have happened to her, we spent 20 minutes thinking the worst. We had no idea where she was and couldn't get hold of anyone from Nakedbus. It was terrifying.
"We had no choice but to put her on this bus because she had a hospital appointment during the day and there was no other way to get her up to us in Auckland. Never in a million years did we expect her to have to go through this kind of ordeal."
Tiffany's father said he accompanied her to Fenton St in Rotorua at 5.15pm, gave the ticket to the driver and reminded him that Tiffany was travelling alone.
He then put her bag in the luggage compartment at the back of the bus and waved goodbye to his daughter as the bus left the station.
In Manukau, Mrs Healey arrived 10 minutes early at the drop-off point at Westfield Mall and watched passengers disembark, but not Tiffany. She saw the driver unloading bags but by the time she went to look for her granddaughter he had closed the doors and driven off.
Mr Healey said a man who was sitting next to Tiffany woke her up and asked her where she was supposed to get off, to which she replied Manukau. He then told the driver the girl had missed her stop.
Mr Healey claims the driver then pulled over on the side of Great South Rd and ordered Tiffany off the bus.
"He just told her to get off - she is 11 and didn't really know what to do so got off.
"She asked about her suitcase and he told her that he had left it in Manukau, which was a lie because my wife went and collected it from the bus depot in Auckland CBD later that evening."
The Healeys say they tried several times to complain to Nakedbus and were told to "send an email".
A spokeswoman for Nakedbus said an internal investigation had been launched and was ongoing.
"The driver has been stood down until the investigation has concluded. Passenger safety is extremely important to us and we are taking this investigation very seriously."