Two other people were badly hurt and nine suffered minor injuries in the crash.
The bus tipped over and landed on its side at around 6 p.m. ET after colliding with a dark grey BMW sedan on 55th Avenue near Lindsay Avenue in the community of Dorval, in the western part of Montreal. At least one other car was damaged in the incident.
The bus driver was in his 50s, police said. His body was pinned under the bus for about four hours until firefighters were able to retrieve it.
The woman who died was in the BMW's passenger seat.
The BMW driver and another bus passenger were taken to hospital with critical head injuries, though both were still conscious, Lamle said.
Five other people with minor injuries were transported to hospital, while four people who were slightly injured declined hospital treatment.
"I was napping on the bus. I had just fallen asleep and then there was a jolt, and I opened my eyes and the whole bus had flipped over on its side," recounted passenger Christopher De Gagné, who said he wasn't hurt. He estimated there were 10 passengers aboard.
"I helped someone get off the bus because they needed help."
Another man at the scene said he was driving by on his way home from work when he saw the bus on its side and people running.
"We saw the driver under the bus. We tried to do something but it was too late," Miguel Mazariegos said. "We saw the woman who survived in the car. She was all bloody. Someone tried to calm her because she was panicking.
"People were leaving the bus on their own. There weren't any paramedics or police, they arrived after. People got out on their own from the bus. Those who could walk got out right away."
The bus belongs to the STM, the Montreal transit corporation. It was on Route 196, which runs from the Côte Vertu metro station south to Lachine.
Accident investigators are still trying to figure out how the crash happened.
The location of the crash is an industrial area two blocks south of the Montreal airport. Cars and trucks often drive quickly along 55th Avenue, a four-lane road that runs through low-lying warehouses and businesses.