The collision, involving the coach and a Ford Focus car, happened on the A272 between Petersfield and Rogate shortly before 08:00 GMT.
The 13 children on board and the driver of the coach are believed to be unhurt.
The woman, 24, who had been driving the car, suffered serious leg and head injuries and has been airlifted to Southampton General Hospital.
Hampshire Constabulary said the children were checked over by paramedics.
The crash happened near the border of Hampshire and West Sussex, near Durford Abbey Farm, between Rogate and Petersfield.
The road was closed between the B2070 London Road in Sheet and the Habin Hill junction in Rogate for about two-and-a-half hours.
It reopened westbound shortly after 10:30 but remained shut eastbound until after 14:00.
Emergency crews from both counties were called to help.
West Sussex Fire & Rescue said its crews used hydraulic rescue equipment to release the woman from the car.
Police are appealing for witnesses.
A woman has been seriously injured in a crash involving a coach carrying school children.