NASA’s OSIRIS-REx mission observed millimeter- to centimeter-scale pebbles being ejected from the surface of asteroid (101955) Bennu, indicating that Bennu is an active asteroid. About 30% of these particles escape from Bennu, and the minimum orbital intersection distance (MOID) between Bennu and Earth suggest the possibility of a ‘Bennuid’ particle flux at Earth. We characterize the evolution of Bennu’s particle stream and potential for meteor flux by simulating weekly particle ejections between the years 1780 - 2135 continuing their dynamical evolution until 2200. Ejections are modelled as a discrete release of 95 particles every week. The meteoroid stream is found to circularize in 80 +/- 40 years. Individual particles and streams remain associable to Bennu for the entire 420 years simulated. Particle flux at Earth is predicted to begin in 2101, as the Bennu-Earth MOID reaches minimum values. The year of highest particle flux, 2182, experiences 161 Earth intersections and accounts for ~1/4 of our predicted meteors. Our methods can be expanded to study the history and structure of the general meteoroid population and to estimate flux from specific near-Earth asteroids.