He began racing in 1931 in a sprint car. He was racing midget cars on the East Coast of the United States at their introduction in 1934. Schindler lost his left leg from above the knee while racing in a Champ car race in 1936 at Mineola, L.I. He is one of three drivers to have participated in the Indianapolis 500 with a prosthetic leg.
Schindler was part of a group determined to keep the AAA out of the East Coast in 1937. He was elected president of the "outlaw" group. Schindler briefly switched to the AAA in 1940, and won the Bronx Coliseum Indoor championship. He returned to his “outlaw” past when he was named the president of the newly formed American Racing Drivers Club (ARDC). He served as president for the club's first six years. Schindler won ARDC championships in 1940, 1945, 1946 and 1948. In both 1947 and 1948 he won 53 midget car feature races.
The Indianapolis 500 was part of the FIA World Championship from 1950 through 1960. Drivers competing at Indy during those years were credited with World Championship points and participation. Bill Schindler participated in 3 World Championship races, but scored no World Championship points.