Roy was born in Detroit, Michigan in 1928. He was educated at the Hollywood Professional School and, as a child actor, appeared in a number of films. He also studied music with Arthur Laage, Joseph Achron, Eada Rubinstein, and Rina Larson.
He composed songs for the nightclub revues Four Below Strikes Back, Dressed to the Nines, Pieces of Eight, Seven Come Eleven, and Dime a Dozen. In addition to Maggie, his theatrical credits included New Faces of 1962, a Broadway revue to which he contributed material; La Belle Helene, an adaptation of Jacques Offenbach's original work; Scandal, which played in Los Angeles; and Special Delivery, which played in Lauderdale Lakes, Florida. Roy also conducted the 1972 revue Everything You Always Wanted to Know About Cole Porter.
In recent years, he remained active on the New York cabaret scene as musical director, arranger, and pianist for singer Julie Wilson. "What a lovely man he was," Wilson told TheaterMania in reaction to Roy's death. "His talent was so enormous. He played for people like Mabel Mercer, Portia Nelson, Ginger Rogers, Celeste Holm, and Marti Stevens. I think his favorite lady in the whole world that he ever worked with was Mary McCarty. To me, Billy was sort of an unsung hero; when he played for me, I just felt like I was soaring. We had a wonderful relationship -- almost 30 years together -- and I loved him very much."