Born in London, and younger brother of the artist Harold Cohen, Bernard studied at St Martin's and Slade School of Fine Art, before teaching at Ealing College and the University of Alberquerque in New Mexico in 1969.
Cohen created staunchly Abstract work from 1957, in reaction against the English semiabstraction artists of the time. Within a few years he had developed a style using linear and organic images, which he proceeded with compositions in which he deliberately merged the boundaries of ground and image. Eventually abandoning the depiction of line altogether, the pieces that followed were made using small disks of color on expanses of white space. These tiled canvases feature predominantly in Cohen's later work.