They said the driver of the car had lost control and it ran off the left side of the road, then off the right side. It struck a guard rail and then struck the bicyclist from behind, the state police said.
The car then ran off the left side of the road, struck a ditch and overturned, according to the police.
The driver fled on foot from the crash scene before law enforcement personnel arrived, the state police said.
They said the bicyclist was not wearing a helmet.
The crash remains under investigation, police said.
Winchester is about 75 miles west of Washington.