  We show that every bundle gerbe on a supermanifold decomposes into a bundle
gerbe over the underlying manifold and a 2-form on the supermanifold. This
decomposition is not canonical, but is determined by the choice of a projection
map to the underlying manifold. Along the way, we prove the familiar
cohomological classification theorems for bundle gerbes and bundle gerbes with
connection in the context of supermanifolds.
