The question of whether a right Hilbert bimodule admits a non-commutative frame bundle-i.e., a C*-algebraic noncommutative principal bundle with which the right Hilbert bimodule is associated via some fundamental representation-is both pivotal and difficult. In this paper, we contribute to this topic by providing an axiomatic characterization of a right Hilbert bimodule, let's say M, that ensures the existence of a unique (up to isomorphism) free C*-dynamical system (A(M), SO(n), alpha(M)) with the property that its associated noncommutative vector bundle, with respect to the standard representation of SO(n), is isomorphic to M. Our approach is inspired by potential applications in noncommutative Riemannian spin geometry.