A student at the Académie des Beaux-Arts in Bordeaux, Bissière settled in Paris in 1909. From 1912 onwards Bissière supplemented his income as a painter with writing exhibition reviews and critics first for 'L'Opinion' and later for 'L'Esprit Nouveau'. These writings formed a solid basis for his personal reflections and offered the necessary references for the development of his own painting.
Having befriended André Lhote and Georges Braque upon his return, Bissière was encouraged to develop a more humanized version of Cubism. As such he enriched orthodox Cubism by applying the fauve technique of heavy brushwork to its usual pictorial vocabulary. Simultaneously, Bissière was engaged by Picasso's researches into advancing Cubism, which brought him to Neo-Classicism. Bissière's unremitting investigations into the survival of Cubism ultimately pushed him to Abstraction during the early 1950s. His studies on Cubism involved a contribution to the first monograph on Braque.
Bissière exhibited with the legendary art dealer Léonce Rosenberg of the Galerie L' Effort Moderne in Paris, 1921-1923, after which he was under contract with Galerie Druet, 1923-1928. In 1964 he represented France at the Venice Biennale. Bissière's authority as a teacher at the Académie Ranson, from 1925 until 1938, is traced in an entire generation of abstract artists including Manessier and Viera de Silva