Washburn is a city and the county seat of Bayfield County, in the U.S. state of Wisconsin. The population was 2,051 at the 2020 census. Th…Washburn is a city and the county seat of Bayfield County, in the U.S. state of Wisconsin. The population was 2,051 at the 2020 census. The city is just east of and adjacent to the Town of Washburn. It is in northern Wisconsin, on the shore of Lake Superior's Chequamegon Bay.