Motivated by the problem of constructing explicit geometric string
structures, we give a rigid model for bundle 2-gerbes, and define connective
structures thereon. This model is designed to make explicit calculations
easier, for instance in applications to physics. To compare to the existing
definition, we give a functorial construction of a bundle 2-gerbe as in the
literature from our rigid model, including with connections. As an example we
prove that the Chern-Simons bundle 2-gerbe from the literature, with its
connective structure, can be rigidified — it arises, up to isomorphism in the
strongest possible sense, from a rigid bundle 2-gerbe with connective structure
via this construction. Further, our rigid version of 2-gerbe trivialisation
(with connections) gives rise to trivialisations (with connections) of bundle
2-gerbes in the usual sense, and as such can be used to describe geometric
string structures.
