The group were on their way to Darlington College when the incident happened on an unclassified road near Piercebridge.
Emergency services including police and a number of ambulances attended the scene.
A police spokesman said around 20 students had sustained minor injuries and were taken to hospitals in the area for treatment.
The driver of the van sustained leg injuries and the bus driver also suffered minor injuries.
North Yorkshire Police said the college had been informed and anyone who had witnessed the crash should contact them on 101.