The OSIRIS-REx mission to asteroid (101955) Bennu resulted in the most detailed and accurate model to date of a small, rubble-pile asteroid. This paper provides a detailed dynamical systems analysis of orbital motion in the vicinity of Bennu, leveraging the final physical model estimated by the science and flight dynamics team. First the dynamics subject solely to the gravitational attraction of the body are explored, detailing the equilibrium points, periodic orbit families and bifurcations between these families. Then the analysis will incorporate the main perturbation from solar radiation pressure (SRP) and survey the basic limits of orbital motion due to this perturbation, and assess the stability of frozen orbits when accounting for the higher-order gravitational field perturbations. This will include the exploration of stable orbits that could be of use to future exploration missions to similar asteroids. The paper will conclude by analyzing the surface dynamical environment of Bennu, including the Roche lobe and other results of interest from a dynamics perspective.