Albert Greene Bates was born on November 30, 1835, in Rhode Island to Reuben and Amy Bates. His father was a pattern maker. He grew up and attended school in Providence, Rhode Island, and he married Edith Ann Haydon in the 1850s. Their son Francis was born on November 15, 1859. They lived in Providence, and Bates also worked as a pattern maker.
Bates received a commission as a 1st lieutenant in Company G of the 1st Rhode Island Infantry, and he mustered in on May 2, 1861. The regiment took part in the First Battle of Bull Run. He mustered out on August 2, 1861. He returned to the Union army soon afterward, mustering in as a sergeant in Company D of the 11th Rhode Island Infantry on October 1, 1861. He was promoted to 2nd lieutenant on March 14, 1863, and he mustered out on July 13, 1863.
Bates returned to Providence after leaving the army, and he earned a living as a carpenter. By 1870, he owned $300 of personal property. He applied for a federal pension in November 1904 and eventually secured one. He died on October 31, 1916.