Fritz Bultman was the second child and only son of A. Fred and Pauline Bultman. His family was prominent in New Orleans, where his father owned a Catholic funeral company. By the age of thirteen he was interested in art, and worked with Morris Graves, who was a family friend. As a high school junior in 1935 Fritz went to study in Munich for two years, and there boarded with Maria Hofmann, the wife of artist and teacher Hans Hofmann. After returning to the United States he studied with Hofmann in New York City and Provincetown, Massachusetts. Despite his father's wishes that he become an architect, with Hofmann's encouragement he decided instead to continue his study of art. In 1944 he bought a house in Provincetown, and thenceforth Bultman and his wife Jeanne divided their time between Cape Cod and New York City.
His early paintings have been described as "rough and painterly", an amalgam of symbolism and geometry.
Bultman was exhibiting with other abstract expressionists by the late 1940s, and in 1950 was aligned with the group of New York School artists, nicknamed the "Irascibles" in an article in Life magazine, who signed a letter to the Metropolitan Museum of Art protesting the institution's conservative policies. With the assistance of a grant from Italy he studied bronze casting in Florence in 1951; subsequently he was the sole abstract expressionist to fully integrate sculpture into his oeuvre.