Paramedics were called to Birchmount and Ellesmere roads just after 1:30 p.m. to treat the woman, said to be in her 40s, who suffered severe injuries.
The woman was transported to a trauma centre for further treatment.
Police said there were no children on the school bus at the time, and the two adults on the bus were not injured.
Investigators from traffic services arrived on scene to piece together how the collision happened.
Police had no update on the woman's condition.