The crash happened at about 1.30pm in Pontefract Road.
The woman, who had been in the car, sustained serious injuries and has been taken by air ambulance to Leeds General Infirmary.
A man in the car was also injured and has been taken to LGI by paramedics.
Passengers in the bus were described as needing treatment at the scene and the fire service was called to deal with a diesel spillage from the bus.
The road is closed and a police spokesman said the closure was likely to be in place for some time.