The 36-year-old victim, named locally as Ross Henderson, was killed walking along a rural road in Kirkliston on Saturday afternoon.
It has been claimed that he tripped and fell into the path of a bus on Path Brae at around 3pm.
Police are investigating the tragedy and have appealed for witnesses to come forward and shed light on events leading up to his death.
They are particularly eager to speak to passengers travelling on board the bus.
Mr Henderson died at Edinburgh Royal Infirmary. No-one else was injured in the collision.
Floral tributes and messages of condolence have been left near at the scene of the accident.