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.

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