Drewry began her political career as a poll worker in 1921. Social issues were a concern to Drewry, and she was interested in uplifting her community. She joined the Northfork Town Council and worked her way up to become the associate chairperson of the McDowell County Democratic Executive Committee. She ran for the House of Delegates in 1948 but was defeated in a tight race after vote count disputes. She ran again in 1950, this time claiming the seat on the legislature. Her victory in the 1950 election made her the first African-American female elected to West Virginia's legislature.
Drewry fought hard for labor and education reform in West Virginia. She was responsible for the introduction of legislation in 1955 which allowed women to serve on juries in West Virginia, the last state to overturn gender discrimination on juries. She was the chairwoman of both the Health and Military Affairs committees and was a member of numerous other social welfare committees. She played a role in exposing attempted bribes from coal companies in her first term of office. Her legislative service lasted thirteen years, the longest of any McDowell County resident at that time. Her groundbreaking success earned her a spot as one of Ebony magazine's top ten Negro women in government in 1956.