Named after his grandfather, William Banks Williams, known in Clinton, KY as "Billy Banks", attended Central School and then Hickman County High School when it was built in 1960. After graduating from high school in 1962, Bill (as he then prefered to be called) attended Memphis State University during the summer, then transfered to Murray State College in Murray, KY in the fall. There he majored in Mathematics and pre-engineering. In 1964 he transfered to the University of Kentucky in Lexington, where he obtained his Bachelor of Science degree in Electrical Engineering in 1967. Bill married Sharon Kay Estes of Winchester, KY in May of 1967. Their son, William Douglas, was born on December 28, 1967. Bill and Sharon were divorced in 1974.

Bill was hired immediately upon graduation by the National Aeronautics and Space Administration (NASA) at John F. Kennedy Space Center in Florida. While there, he worked on many of the major space programs from 1967 through 2000. He was on the test teams of the Apollo Program, the Apollo-Soyuz Program, the Skylab Program, the Viking Program that landed 2 unmanned probes on Mars, and the Space Shuttle Program. Bill retired from NASA on January 3, 2001.

Bill met his wife, Sandra Sheilagh Johnstone, in Lancaster, CA in 1976 where he was working on the Approach and Landing Test Program, an early Space Shuttle test program. They were married in Palmdale, CA on October 29, 1977, and moved to Titusville, FL in December of that year.

Sandra, the daughter of Ivan and Sheila Johnstone, was born and raised in Australia. Her family immigrated to America when she was 12 years old. Living in Palmdale, CA, "Sandy" attended Antelope Valley College and became a Registered Nurse, practicing in hospitals in Los Angeles, Lancaster, and Chicago, before returning to Palmdale. After marrying Bill and moving to Florida, she obtained her Bachelor of Science degree in Nursing and her Certificate in Judaic Studies from the University of Central Florida, and is now a Board Certified School Health Nurse.