The bus operator said the vehicle had been on its way to Homewood School in Tenterden.
A Kent Police spokesperson said: “Officers attended and remain on scene to assist while passengers leave the bus and the vehicle is recovered.
“Paramedics attended as a precaution. There were no reported injuries.”
Kent Fire and Rescue Service sent three fire engines to the scene.
In a statement, the fire service said: “The cause is believed to be the vehicle slipping on black ice.
“Crews are reminding everyone to use extra caution when driving in cold temperatures as there could be black ice on the roads, so avoid sudden braking and leave plenty of space between you and the vehicle in front.”
Stagecoach South East managing director Joel Mitchell confirmed there had been an incident on the A28 and said: “There are currently no reported injuries.
“Stagecoach is cooperating fully with the local authorities, and the circumstances surrounding the incident are under review.”
He said: “Our driver responded calmly and professionally, and I am very grateful for his actions in ensuring the safety of all passengers during a challenging incident.”