The steel–concrete composite structure is widely used in civil engineering for large-span bridges. Orthotropic steel bridge decks (OSDs) have particularly gained popularity due to their excellent mechanical performance. To address cracking issues in OSDs and concrete in negative moment regions, a novel bi-directional U-ribbed stiffening plate (BUSP)–concrete composite bridge deck is proposed. By using finite element analysis, the mechanical performance is evaluated based on maximum tensile stress and vertical displacement of concrete overlays. Results show that the BUSP–concrete deck outperformed conventional flat decks. It is also found that increasing the height, thickness, and opening width of U-ribs reduced tensile stress and maximum displacement. Adjusting height had the most significant effect on displacement while opening width affected tensile stress the most. Considering material usage, optimizing height is proved to be more effective than adjusting thickness and opening width. Decreasing spacing parameters improved performance but added complexity and reduced construction convenience. These findings will guide the design and optimization of steel–concrete composite bridge deck structures.