Educated at New York University, he first worked at an advertising agency in New York until the early 1960s, when he founded the film production company Videocraft International (now called Rankin/Bass) with Arthur Rankin, Jr. He is best known for his collaborations with Arthur Rankin, Jr., co-directing and producing a wide array of stop motion animated features and cartoons. He composed the score for some of these films, collaborating with Maury Laws. Bass also served as lyricist for several songs. He has also solo directed some Rankin/Bass features, such as Mad Monster Party (1969) and The Daydreamer (1966).

Bass stopped directing and producing films in 1987, but most recently he has written a series of children's books, based around the character of "Herb, the Vegetarian Dragon". As of 2005, he splits his time between New York City, his home in the Hudson Highlands, and Paris.