"There were no evident signs of homicidal violence," said police spokesman Jim Sughrue. "The remains will be examined by the medical examiner to determine a cause of death."
The North Carolina Center for Missing Persons issued a Silver Alert for Bishop on Sunday.
Bishop, who was believed to be suffering from dementia or some other cognitive impairment, was last seen around 6 p.m. Saturday at 5708 Setter Circle in Raleigh.
Developed in 2007, Silver Alert is a system that quickly notifies the public about missing endangered adults who suffer from dementia or other cognitive impairments, such as Alzheimer's disease.
It also allows caregivers and nursing homes to report a person missing. In the past, only a family member could report an adult missing.