Bevan studied at the Westminster School of Art, and at the Académie Julian in Paris. In 1894 he visited Pont-Aven in Brittany, where he met Gauguin and Renoir, and saw Cézanne’s work. He married Stanislawa de Karlowska, a Polish painter, and with her made frequent visits to Poland.
In 1911 Bevan was a founder-member of the Camden Town Group. He was also a member of the Fitzroy Street group and the New English Art Club. He made regular painting trips to Somerset with Charles Ginner and Frederick Spencer Gore. Bevan was a great lover of horses, and the horse sales and stable-yards of the Barbican, near where he lived, provided him with much of his subject-matter. Memorial exhibitions for him were held at the Goupil Gallery and at Brighton Art Gallery in 1926, and a Centenary Exhibition of his work was held at the Ashmolean Museum in Oxford and at Colnaghi’s in London in 1965.