The full coach carrying almost 50 pupils had pulled over to the side of the road when the grassy verge gave way.
The 14-year-old pupils - many with cuts and broken bones - managed to crawl from beneath the bus but the woman driver had become trapped and had to be cut free by fire fighters.
She suffered chest and abdominal injuries and was later reported to be in intensive care.
All passengers were assessed by ambulance crews at the scene on Holme Lacy Road following the incident at 8.20am this morning, and the female driver and 25 pupils were taken to Hereford County Hospital for treatment.
An ambulance spokesperson said the driver and six pupils who had suffered the worst injuries were taken away by ambulance.
A further 19 children with minor injuries were brought to hospital via other means.
The arrival of such a large number of injured children at hospital, many covered in mud and bleeding, was described as a 'distressing scene' by one doctor at Hereford County.
Dr Malcolm Russell told Sky News there were 'a number of potentially seriously injured casualties', adding: "A lot of children were covered in mud, a few of them were bleeding.
"We're just very glad that the vast majority of children involved have minor injuries."
The children are thought to have been travelling to Bishop of Hereford's Bluecoat School, a comprehensive secondary, and nearby St Mary's Roman Catholic High School.
Sara Catlow-Hawkins, headteacher at Bluecoat School, confirmed that four of the school's pupils were involved in the accident and said they had all 'behaved and worked with each other in a tremendously supportive way'.
She said: "Both schools would like to say that our prayers go out to the driver and her family."
A spokesperson for PW Jones Coaches, which operates the bus, said witnesses claimed that a lorry involved in the accident did not stop.
She said: "A coach that was carrying schoolchildren went off the road and the children are saying that a lorry was involved and didn't stop.
"The coach had pulled over to stop on a grass verge and it gave way."
Dr Paul Harris, whose son was on the bus, told BBC News: "I've heard that all the kids are alive and there are some that have got broken bones. So it's much better than it could have been."