Leeds United fan Stephen Doherty, 63, died from head injuries shortly after getting off the number 13 bus in Middleton on Boxing Day.
The bus was turning around at the terminus on Middleton Park Avenue and was on its way back to the depot when the incident happened at about 5.50pm.
The 48-year-old man who was driving the bus was arrested on suspicion of dangerous driving and is on bail pending continuing enquiries.
Investigating officers have now issued a CCTV picture of a woman who was also travelling on the bus and may have seen the collision.
West Yorkshire Police’s major collision enquiry team has appealed to her to contact them.
Det Sgt Carole Greaves said; “We are continuing to investigate this incident and are appealing for anyone who witnessed the collision which resulted in Mr Doherty’s death to come forwards.
“In particular we would like to speak to the lady pictured as, due to her position on the bus, we believe she may well have witnessed what took place.”
In a statement members of Mr Doherty’s family expressed their loss at his death.
The statement said: “We would like to thank all Steve’s friends and colleagues at [builders’ merchants] Selco for their kind love and support since his death on Boxing Day.
“We are also touched by the many messages left for him, from people who we didn’t know. He will be greatly missed by all who knew him.
“Steve enjoyed following his football team, Leeds United, and going out drinking with his friends. He loved his work at Selco and family gatherings. He’s sadly gone too soon.”
First bus, which operates the number 13 service, is helping police with their enquiries.
Anyone with information should call the major collision enquiry team on 101.