Educated at Columbia University,Bessie became initially known for his translations of avant-garde French literature,including Songs of Bilitis by Pierre Louÿs and The Torture Gardenby Octave Mirbeau.He later fought as a volunteer in the Abraham Lincoln Brigade during the Spanish Civil War.

No stranger to soldiering, Bessie had been a member of the International Brigades, and fought against Franco's forces in the Spanish Civil War in 1938. Upon his return, he wrote a book about his experiences, Men in Battle. About the book, Ernest Hemingway commented:

A true, honest, fine book. Bessie writes truly and finely of all that he could see ... and he saw enough.

Bessie wrote screenplays for Warner Brothers and other studios during the mid and late 1940s. He was nominated for an Academy Award for Best Original Story for the patriotic Warner's film Objective Burma (1945).

His career came to a halt in 1947, when he was summoned before the House Un-American Activities Committee (HUAC). He refused to deny or confirm involvement in the Communist Party USA, and in 1950, he became one of the Hollywood Ten when he was imprisoned and blacklisted. After his release from prison, he worked at the hungry i nightclub in San Francisco, running the lights and sound board and frequently introducing performers.

In 1965, Bessie wrote a book about his experience with the HUAC, Inquisition in Eden. He wrote another book in 1975, Spain Again, which chronicled his experiences as a co-writer and actor in a Spanish movie of the same name (Spain Again, 1969).

His screenwriting career was ruined by the blacklisting, and he never returned to Hollywood. Late in is life, however, he was involved in bringing his novel Bread and a Stone to the screen in the feature film "Hard Traveling" (1986) starring J.E. Freeman and Ellen Geer. The screenplay for the film was written by one of Alvah's two sons, Dan Bessie, who has also spent his career working in the film industry. Dan Bessie has published some of his father's previously unpublished or uncollected works, notably his Spanish Civil War Notebooks (2001).

In his family biography Rare Birds: An American Family (University Press of Kentucky, 2001), Dan Bessie notes that Alvah was related to some highly successful entrepreneurs: he was father-in-law of well-known 1960s poster artist Wes Wilson, husband of Alvah's daughter Eva, and a brother-in-law (through his first wife, Mary) of famous advertising executive Leo Burnett.

Bessie died in Terra Linda, California, aged 81.