He went from the drawing school in Dole to Gustave Moreau's studio in the École des beaux-arts de Paris, where he met and became friends with Henri Matisse.
In 1901 Bussy visited London, where he came into contact with members of some English artistic circles, especially the Bloomsbury Group, and where he met Dorothy Strachey, who became his wife in 1903.
Shortly after the wedding Simon and Dorothy moved to Roquebrune Cap Martin, in the south of France, where they bought a small house that soon became a meeting point for both French and English artists, writers and intellectuals.
In addition to Dorothy's brother, the historian Lytton Strachey, and his cousin, the painter Duncan Grant, others included Rudyard Kipling, André Gide, Roger Fry, Vanessa Bell, Mark Gertler, Paul Valéry, Virginia Woolf, and Bernard Berenson.
Later he devoted himself almost exclusively to animals, especially birds, reptiles and fish, and would observe and study them at London Zoo.