William Bluford Adamson was born in Prairie Grove, Texas, on January 24, 1904. His grandparents were Reverend William Paxton Gillespie and Mary Catherine "Kate" Gillespie, faculty members at Trinity University when it was founded in 1869. His parents, Pearl Gillespie and Frederick Richmond Adamson, met as students at Trinity in the late 1800s. William had a brother, F. Lawrence Adamson, and a sister, Mary Catherine Adamson Bynum. Adamson married Lucile Larsen, a nurse, in 1929; she passed away in 1959. His second wife, Sadie Lucille, passed away in 2009.
Adamson graduated from Trinity University in 1924, and attended medical school at Vanderbilt University. Following internships at Vanderbilt University Hospital and Barnes Hospital in St. Louis, he settled in Abilene, Texas, where he opened a cardiology office in 1929. Adamson served as a lieutenant colonel in the United States Air Force during World War II. After his service, he continued to practice medicine in Abilene until 1968. Adamson served as president of the Taylor Jones County Medical Society, a diplomate of the American Board of Internal Medicine, a fellow of the American College of Physicians, and a fellow of the American College of Cardiology. He was the recipient of the Gold Headed Cane award from the Taylor Jones County Medical Society in 1963 and the Paul V. Ledbetter Award in 1973. His widow Sadie established the William B. and Sadie L. Adamson Charities Foundation to support arts groups in Abilene.