The incident took place on the A227 Shipbourne Road at around 4.45pm. The bus collided with the wall outside Manor House, one of the boarding houses of the public school.
The 208 bus was on the way to East Peckham. An ambulance attended the scene and the driver, who was said to be in a state of shock, received treatment.
A witness said the bus struck a car coming in the opposite direction at a point where parked cars make the carriageway narrow.
The bus caught the kerb and then the driver appeared to lose control, swerving into the wall.
Bystanders helped the passengers from the bus and they were invited into the school while the children contacted their parents to be picked up.