Billy was the son of Greek immigrant restaurateur Gus Pappas. He and his mother Kula arrived in the United States aboard the New Greece when he was 16, meeting his father for the first time. When he was old enough, and had learned enough English, Pappas enlisted in the U. S. Navy. He served as a tanker gunner in the Pacific theater. As soon as he returned he proposed to his girlfriend Katina.
Pappas continued in restaurant work and, after seeing his three children through college, opened his own Mr Hot Dog stand on 19th Street North in Bessemer. He operated the business for over 30 years before retiring.
Shortly afterward, Pappas was diagnosed with prostate cancer. He died in July 2009 soon after attending his granddaughter's wedding. He was survived by his wife, three children and two grandchildren. His funeral services were held at the Holy Trinity-Holy Cross Greek Orthodox Cathedral and he was buried at Elmwood Cemetery.