Dover is a city in Bonner County, Idaho. The population was 556 at the 2010 census. According to the United States Census Bureau, the cit…Dover is a city in Bonner County, Idaho. The population was 556 at the 2010 census. According to the United States Census Bureau, the city has a total area of 3.24 square miles, of which, 3.22 square miles is land and 0.02 square miles is water.