William Bostick spent time in Chicago with his Aunt Tillie, who sent him to classes at the Art Institute. In 1934, he earned a BA degree in graphic arts from the Carnegie Institute in Pittsburg, and was much influenced by Porter Garnett from whom Bostick learned the skill of hand-printing books. Following this, he worked briefly for the National Recovery Act and as a typesetter and in 1935, he began study at the Detroit Academy of Art where an influential teacher was Carlos Lopez. In 1936, he exhibited his first painting, and the venue was an exhibition sponsored by a Michigan artists group. He briefly attended an Arts and Crafts School, and in 1937, enrolled in Cranbrook Academy where Zoltan Sepensky was a strong influence as was Maja Grotell from whom he studied ceramics.

His education at Cranbrook was interrupted by his navy service in World War II. He spent much time in France and was a decoder and coder and military-map artist for invasions including Normandy. After the war, he and his wife, Mary Jane, had their first baby, and he began his job at the Institute of Arts. He also continued to study ceramics, this time at Wayne State with John Foster, and in 1954, Bostick received an MA degree in art from Wayne State.

He was also a book illustrator and author, and his books included "Many a Watchful Night", 1945, which he also co-authored; "The Amphibious Sketch", 1945, of which he was author and illustrator; "England Under GI's Reign", 1946, illustrator; and "Mysteries of Blair House", 1948, illustrator.