The hyporheic zone is a transition zone for the exchange of matter and energy between surface water and subsurface water. The study of trends and sensitivities of bed hyporheic exchanges to the various influencing factors is of great significance. The surface−groundwater flow process was simulated using a multiphysics computational fluid dynamics (CFD) method and compared to previous flume experiments. Based on that, the single-factor effects of flow velocity (u), water depth (H), dune wave height (h), and bed substrate permeability (κ) on hyporheic exchange in the bed hyporheic zone were investigated. The sensitivity analysis of various factors (H, u, dune wavelength (L), h, bed substrate porosity (θ), κ, and the diffusion coefficient of solute molecules (Dm)) in the surface−subsurface water coupling model was done using orthogonal tests. The results indicated that u, h, and κ were positively related, whereas H was negatively related to hyporheic exchange. H and u showed large effects, whereas κ, Dm, and θ had moderate effects, and L and h showed small effects on hyporheic exchange. This study provides valuable references for the protection and recovery of river ecology.