Vancouver police spokesman Const. Brian Montague said the accident happened shortly before 6:30 p.m. PT, on Hastings Street just west of Main Street.
"It is still early in the investigation, but it appears the victim fell under the bus as it pulled away from the bus stop," Montague said in a written statement.
Several people who witnessed the woman fall called 911, bus the bus driver and the passengers were not aware at first of what had happened.
The driver pulled over and stopped the articulated bus a short time later further west along Hastings Street, Montague said.
The woman was pronounced dead at the scene. Police said Sunday they did not know her identity.