The 51-year-old man suffered "significant" head and arm injuries in the accident in Colinton Mains Drive, Edinburgh, at about 8.20pm yesterday.
It happened shortly after a Lothian Buses number 4 bus set off from a stop next to a Tesco store, police said.
The man was taken to the Royal Infirmary of Edinburgh before being transferred to the Western General, where he remains in a serious condition.
Sergeant Brian Smith said: "At this time we are trying to establish exactly what happened during this incident, which has resulted in a man sustaining serious injuries.
"Motorists and members of the public who were in the area at the time and have information relevant to our investigation are asked to contact police immediately."