Basye is a census-designated place in Shenandoah County, Virginia, United States. The population was 1,374 at the 2020 census. As of the 2000 census, the CDP was known as Basye-Bryce Mountain. Basye was named after a local family that lived in the area and whose cemetery remains off one of the holes on the golf course. Originally considere…Basye is a census-designated place in Shenandoah County, Virginia, United States. The population was 1,374 at the 2020 census. As of the 2000 census, the CDP was known as Basye-Bryce Mountain. Basye was named after a local family that lived in the area and whose cemetery remains off one of the holes on the golf course. Originally considered part of the Orkney Springs community, Basye was named by Martha Basye, married to William Brice, who opened the original resort. One of the early settlers seems to have been John Basye.