The bus veered of the road, went down a banking and into a garden
The bus left the A641 Bradford Road and crashed into a garden between Dewhurst Road and Fartown Green Road at 1000 BST on Monday, police said.
Five ambulances were sent to the crash scene, and paramedics treated passengers at the roadside for injuries including whiplash, cuts and bruises.
The bus driver was treated for shock and minor injuries.
None of the injuries were believed to be life-threatening, but a number of patients were transferred to hospital, an ambulance spokeswoman said.
The road was closed after the accident and diversions were in place. Police urged drivers to avoid the area if possible.