When Alexander Bates was born on 22 January 1793, in Bowdoinham, Sagadahoc, Maine, United States, his father, Frederick Bates, was 21 and his mother, Elizabeth Campbell, was 24. He married Mary Starbird on 3 November 1814, in Bowdoinham, Lincoln, Maine, United States. They were the parents of at least 2 sons and 5 daughters. He lived in Richmond, Lincoln, Maine, United States in 1850 and Richmond, Sagadahoc, Maine, United States in 1860. He died on 1 January 1883, in Bowdoinham, Sagadahoc, Maine, United States, at the age of 89, and was buried in Litchfield Plains Cemetery, Litchfield, Kennebec, Maine, United States.