Here, we study the dynamical effects of the solar radiation pressure (SRP) on a spacecraft that will survey the near-Earth rotating asteroid (101955) Bennu when the projected shadow is accounted for. The spacecraft's motion near (101955) Bennu is modelled in the rotating frame fixed at the centre of the asteroid, neglecting the Sun gravity effects. We calculate the SRP at the perihelion, semimajor axis and aphelion distances of the asteroid from the Sun. The goals of this work are to analyse the stability for both homogeneous and inhomogeneous mass distribution and study the effects of the SRP in equatorial orbits close to the asteroid (101955) Bennu. As results, we find that the mascon model divided into 10 equal layers seems to be the most suitable for this problem. We can highlight that the centre point E8, which was linearly stable in the case of the homogeneous mass distribution, becomes unstable in this new model changing its topological structure. For a Sun initial longitude ψ 0 = −180 • , starting with the spacecraft longitude λ = 0, the orbits suffer fewer impacts and some (between 0.4 and 0.5 km), remaining unwavering even if the maximum solar radiation is considered. When we change the initial longitude of the Sun to ψ 0 = −135 • , the orbits with initial longitude λ = 90 • appear to be more stable. Finally, when the passage of the spacecraft in the shadow is accounted for, the effects of SRP are softened, and we find more stable orbits.