Mrs Kirby said the children were frightened they might "end up in the (Grey) river".
"It was a frightening experience and if the students had not have taken control the outcome could have been horrific."
Another parent, Fiona Lawton, said the driver appeared to be in trouble before he had even left the high school about 3.15pm.
"According to my teenagers, when the driver pulled out from the school he rolled it back into another bus."
He failed to stop at a stop sign at a state highway intersection and banged into road pegs on a straight stretch of road.
She did not want to get the driver into trouble, "because he was a nice old man."
The Greymouth Star understands the 82-year-old driver told Ritchies he was unwell yesterday but was told no one was available to replace him.
Wendy McLennan, who had two children on the bus, said it was a scary incident, especially for her youngest son.
"I understand the driver had reported to the company that he was sick, but they didn't have a replacement. The company are responsible for what happened."
Other parents said one of the children was so scared he demanded to be let off at Dobson.
Grant Soeters said it was not only the trip home that was a problem - the trip to school "wasn't that uneventful either".
"The driver was weaving all over the road on the morning trip, and at Dobson he went too close to the left-hand side of the road, over-corrected and ended up on the wrong side of the road."
Mr Soeters said the incident yesterday was the last straw.
"There have been issues prior to this and it has to be dealt with."
Ritchies Greymouth workshop manager Greg Harris confirmed there had been an "incident", which was being investigated.
He would not comment when asked whether the driver had been stood down but did say he was "not driving today".
Attempts to contact Ritchies managing director Andrew Ritchie in Auckland were unsuccessful.
Greymouth police said they were investigating.