At 5.50pm on Friday, police were called to a collision involving a double-decker bus and a 63-year-old man in Middleton Park Avenue at the junction with Throstle Road.
The injured man, who was pronounced dead at the scene, was a passenger who had just got off the Number 13 service which terminates at that point.
The collision is believed to have occurred as the bus set off to turn around to face back up Middleton Park Avenue.
Detective Sergeant Carole Greaves, of West Yorkshire Police’s Major Collision Enquiry Team, said:
“We would like to hear from anyone who witnessed the incident, as we try to establish the full circumstances that led to this man’s death.
“We are particularly keen to trace a potential witness who was a female passenger who we believe left the bus at the same time as the deceased.”
Anyone with any information is asked to contact the Major Collision Enquiry Team via 101.
A 48-year-old man has been arrested on suspicion of causing death by dangerous driving. He was released on police bail pending further enquiries.