Police inspect the bus in the ditch.
The bus veered into a ditch and stopped on a steep angle.
The cause of the crash is not yet known but police said last night that they wanted to speak to the driver of a white sedan that was travelling along the road in the opposite direction at the time of the crash.
"The bus just sped off the side of a bank," Taumua said.
He was sitting in a left-side window seat near the back and suffered several deep gashes to his left shoulder when the window smashed in the accident.
"Everyone flew over to the other side of the bus," Taumua said.
"A lot of kids were screaming."
Some boys at the back of the bus kicked out the back window and it was through this that everyone got out, after clambering half on the floor and half on the seats to get there. It took about five minutes to get everyone out.
Taumua said he helped people to get out through the emergency exit - the only way out. His shoulder was bleeding "quite badly" and a jacket was used to stop the blood loss.
At hospital he received stitches and said last night his shoulder was still painful.
His friends were okay, but "people are still shocked about what happened".
Taumua's parents, Bob and Marian Belford, picked him up from Howick College around 5.30pm after he arrived with other injured students from Thames in a van. Uninjured students had returned on buses earlier.
Watch: School bus crash injures 14
Another parent of a child injured in the crash said she found out about the crash through the media.
"I firstly phoned the school after I had seen it on the media, and we hadn't been contacted by the school. They said to me that they were waiting for more facts.
"I'd had a call from my daughter, she was hysterical, she was crying, she told me she'd been hurt and she was in a crash."
The mother said she spoke to a paramedic who was treating her daughter and was told a senior paramedic was needed to assess her because she was complaining of neck pain.
She had initially waited at Howick College for her daughter to arrive because she said she was told her daughter wasn't injured and would be coming back earlier.
"The bus arrived 20 minutes later and my daughter wasn't on board ... I just lost it, I totally cracked."
She found out her daughter was in hospital when a friend went to pick up a child from Thames Hospital.
Principal Iva Ropati could not be reached for a response to the mother's claims last night.
He earlier said parents were "distraught" at the news of the crash.
"They have all been contacted and obviously it's a shock to them but we have the support team here to try and support them as much as possible."
Watch: School bus crash: Parents 'distraught'
Charge nurse manager for Thames Hospital David James said students arrived at the hospital cold and shocked.
"On a day like today you can get hypothermia very quickly," he said.
"There were a few that needed x-rays and others that had cuts to their arms and bumps and bruises, but all in all they're not serious."
Cellphones weren't allowed on camp, so when the students arrived at hospital it had been a challenge for them to reach their parents, he said.
Ian Coatsworth, the Ministry of Education's services manager for Waikato, said of the students: "They're laughing and showing off their battle wounds. But you can still get a sense that this has been quite an event for them, and we are providing them support for that."
Acting Sergeant Rachel Holmes said police were still unsure what caused the crash.
