Salt marsh systems require a net import of inorganic sediment to maintain their structure in response to sea‐level rise. Marshes are affected by physical processes including tides, waves, sediment transport, and the influence of vegetation, and these processes interact in complex ways leading to sediment accretion or erosion. We implement a 3‐D hydrodynamic sediment transport model in an idealized marsh‐bay complex with a gently sloping edge, and use it as a laboratory to explore the processes leading to bed elevation change through the bay‐marsh continuum. We use the novel equadratures method for efficient sensitivity analysis to test the roles of wave, vegetation, and sediment parameters on wave dissipation, bed shear stress, sediment fluxes, and deposition and erosion across a transect spanning bay shallows to the marsh. Within the explored bounds of parameter uncertainty, significant wave height (H_sig), settling velocity (w_s), and critical shear stress (τ_crit) most strongly affect accretion on the marsh platform. Deposition is affected more by parameter‐parameter interactions, that is, both τ_crit and w_s or both H_sig and w_s, than by a single parameter varying alone. The sediment that accretes on the marsh platform originates beyond the marsh edge, indicating that the dynamics of the adjacent mudflat are important for predicting the fate of the marsh. Applying efficient sensitivity analysis techniques can empower process‐based models to test more parameters, larger ranges, and longer timeframes, enabling future predictions of marsh response to sea‐level rise based on physical processes