The incident happened at around 8.25pm last night and although enquiries are ongoing, it is believed the 64-year-old got off the bus on Albion Street in Castleford, next to the bus station, and fell in front of the single-decker.
The bus then set off and was in collision with the pedestrian, who sustained fatal injuries as a result.
The road was still closed off this morning.
Officers are appealing for anyone who witnessed the incident or anyone who was driving in the area at the time of the collision and may have dash cam footage of the incident to get in touch with police.
Anyone with information is asked to contact the Major Collision Enquiry Team on 101, quoting log number 1829 of October 9.