When Alanson Bicknell was born on 29 February 1836, in Exeter, Washington, Rhode Island, United States, his father, Benjamin Bicknell, was 36 and his mother, Mary Elizabeth Wells, was 37. He married Catherine C. Sweet about 1855. They were the parents of at least 6 sons and 1 daughter. He died on 31 October 1871, in North Kingstown, Washington, Rhode Island, United States, at the age of 35, and was buried in North Kingstown, Washington, Rhode Island, United States.