Bancroft is a city in Kossuth County, Iowa, United States. The population was 699 at the time of the 2020 census. Bancroft was platted in 1881…Bancroft is a city in Kossuth County, Iowa, United States. The population was 699 at the time of the 2020 census. Bancroft was platted in 1881. It was named for George Bancroft, an American historian, government official, and diplomat.