St Mary's College principal Sarah Dwan said it was fortunate that a staff member was in a car behind the stricken coach and was able to offer immediate help this morning.
"All our students are safe and well, and we are incredibly proud of how they have reacted and responded.
"Support is being provided for the students and their families and we will continue to support all involved.
"A staff member happened to be behind the bus on their way to school who was able to stop and provide support to our students."
Dwan said the high school was grateful for the response of emergency services and the bus company.
A total of 24 people were assessed for injuries after the single-vehicle crash in Newton Rd just after 8am.
A St John spokeswoman confirmed one person was taken to Auckland City Hospital with minor injuries.
The crash caused extensive traffic delays through Khyber Pass Rd and in the suburb of Ponsonby.
The Newton Rd overpass was expected to remain partially closed for "some time this afternoon" as teams inspected and worked on repairing damage to the wrecked barrier.
Auckland Transport said the vehicle recovery operation was complete but motorists were unable to use westbound lanes.
The Coachways NZ bus crashed through iron gates and came to a rest wedged on the footpath on the bridge above the Northwestern Motorway.
Photos and footage show its front half hanging over the bridge. Both directions of the overbridge were closed as the bus was recovered.
Firefighters had to cut parts of the fence. An inflation device was placed under the bus to raise it up and then winch it to safety.
A staff member at the company referred inquiries to their boss, who was unavailable as he was at the crash scene.
'It looked precarious'
Waitematā local board member Glenda Fryer was heading to Newmarket to hand out election leaflets when she came across the crash.
She believes she arrived about a minute after the incident happened, as the children on the bus were starting to get off the bus and emergency services had not arrived yet.
"The kids on the bus were filing out. There wasn't anyone weeping or panicking.
"I was very worried that someone had been injured, [but] there was no one crying or screaming.
"But it looked rather precarious, especially if you were at the front of the bus."