Bussy was born in Dôle in the Jura region in 1870, to parents of peasant stock. He won a scholarship to study art and went to Paris in 1886, to the École des Arts Décoratifs. In 1890 he moved to the École des Beaux-Arts, where he studied under Delaunay and Gustave Moreau, and made life-long friendships with Matisse and Rouault. He was strongly influenced by Degas, Whistler and Japanese prints.
Bussy’s first one-man exhibition was at the Galerie Durand-Ruel, Paris, in 1897, with another in 1899. He first visited London in 1901, and was introduced to fellow artists and the New English Art Club through his friend, William Rothenstein. He married Dorothea Strachey, sister of Lytton Strachey, in 1903 and afterwards lived in Roquebrune in the South of France, spending the summers in England and Scotland. Through the Strachey connection he knew many members of the Bloomsbury group, and made portraits of Paul Valéry, André Gide and others. Later he turned mainly to landscapes, but is perhaps best known for his small studies of birds, animals and fishes, for which he made many sketches at London Zoo. In 1965 he had an exhibition of sixty-two of these works in pastel, as well as forty paintings. He died in London in 1954.