The incident happened at around 9am on Tuesday on the B725 road near Bankend, Dumfries.
The single-decker coach was being driven by a 59-year-old man from Dumfries and had 22 students on board, travelling to Dumfries College.
Seven people received minor injuries and three were taken to Dumfries and Galloway Royal Infirmary for treatment for injuries including cuts and bruises.
The driver was treated at the scene, police said.
Constable Stuart Delaney said: “The cause of the crash is still being investigated and we are keen to hear from anyone who may have witnessed it.
“The road at the scene was closed until the bus was recovered.
“The students who were uninjured were later taken on to the college.”