In this work, we study the dynamics of particles around Bennu. The goal is to understand the stability, evolution, and final outcome of the simulated particles around the asteroid. According to the results, the particle sizes can be divided into two main groups depending on their behavior. Particles smaller than a centimeter are quickly removed from the system by solar radiation pressure, while the dynamics of particles larger than a few centimeters is dominated by the gravitational field of Bennu. Because of its shape and spin period, Bennu has eight equilibrium points around it. The structure of the phase space near its equatorial surface is directly connected to these equilibrium points. Therefore, we performed numerical simulations to obtain information about the orbital evolution near the equilibrium points. The results show that most of the particles larger than a few centimeters fall in the equatorial region close to the Kingfisher area or close to the region diametrically opposite to it. In contrast, almost none of these particles fall in the equatorial region close to the Osprey area. In addition, we also performed computational experiments considering a spherical cloud of particles initially orbiting Bennu. Most of the particles in prograde orbits fall on the surface within our integration period, which was limited to 1.14 years. The particles preferentially fall near high-altitude regions at low equatorial latitudes and close to the north pole. The mid-latitudes are those more depleted of falls, as in the Nightingale and Sandpiper areas.