This numerical study evaluates the concept of a combined mesh-plate bumper as a shielding system protecting unmanned spacecraft from small (1 mm) orbital debris impacts. Two-component bumpers consisting of an external layer of woven mesh (aluminum or steel) directly applied to a surface of the aluminum plate are considered. Results of numerical modeling with a projectile velocity of 7 km/s indicate that, in comparison to the steel mesh-combined bumper, the combination of aluminum mesh and aluminum plate provides better fragmentation of small hypervelocity projectiles. At the same time, none of the combined mesh/plate bumpers provide a significant increase of ballistic properties as compared to an aluminum plate bumper. This indicates that the positive results reported in the literature for bumpers with metallic meshes and large projectiles are not scalable down to millimeter-sized particles. Based on this investigation’s results, a possible modification of the combined mesh/plate bumper is proposed for the future study.