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 and 2135 continuing their dynamical evolution until 2200. Ejections are modeled as a discrete release of 95 particles every week. The meteoroid stream is found to be fully distributed around Bennu's orbital path 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.