Dr. Drewry was born in Southampton County, Virginia, attended Randolph-Macon College, and graduated from the Medical College of Virginia in 1884. He served at the Central State Hospital (1886–96) and was appointed superintendent in 1896, remaining in the post until 1924. Dr. Drewry then became City Manager of Petersburg (1924–29), following which he served as head of the Mental Hygiene Department of the Public Welfare Division of the State of Virginia.
He was a member of several medical societies, including the National Committee for Mental Hygiene. Dr. Drewry was President of the American Medico-Psychological Association (1909–10).