Bevan was born in Bradford, Yorkshire. He studied at Bradford School of Art from 1968 to 1971, followed by Goldsmiths' College, London from 1971 to 1974, and the Slade School of Fine Art from 1974 to 1976. He was elected to the Royal Academy of Arts in London as an Academician in 2007.
Bevan came to prominence as an artist in the 1980s, taking part in the ICA show Before it hits the floor in 1982, Problems of Picturing, curated by Sarah Kent and held at the Serpentine Gallery in London in 1982-83, and The British Art Show, a touring exhibition of contemporary art, in 1984. This was followed by exhibitions mainly in the USA and Germany, including the LA Louver Gallery, California, in 1989, 1992 and 1995, and Kunsthalle, Kiel, in 1988, Staatsgalerie Moderner Kunst Haus der Kunst, Munich, in 1989, and Galerie Wittenbrink, in Munich, during the 1990s. Bevan also exhibits in Australia, at Niagara Galleries, Melbourne and Liverpool Street Gallery, Sydney, with recent solo shows in 2013.
In 2006 Bevan was invited to explore the printmaking technique of monoprints, a technique he had not previously tried, at the Scuola de Grafica in Venice. This resulted in over 80 images which were subsequently shown in London, and marked the beginning of an interest in printmaking Bevan retains to this day.
Bevan has work in many major art collections around the world, including Arts Council England, the Israel Museum, Jerusalem, the British Museum, the Louisiana Museum in Denmark, Museum of Contemporary Art, Los Angeles, the Museum of Modern Art, New York and the Tate.
