Bingen is a city in Klickitat County, Washington, United States. The population was 778 at the 2020 census. Bingen was founded by P.J. …Bingen is a city in Klickitat County, Washington, United States. The population was 778 at the 2020 census. Bingen was founded by P.J. Suksdorf in 1892, and named by him for Bingen am Rhein in Germany. Bingen was officially incorporated on April 18, 1924.