The proposed Surface Water and Ocean Topography (SWOT) mission would provide measurements of water surface elevation (WSE) for characterization of storage change and discharge. River channel bathymetry is a significant source of uncertainty in estimating discharge from WSE measurements, however. In this paper, we demonstrate an ensemble‐based data assimilation (DA) methodology for estimating bathymetric depth and slope from WSE measurements and the LISFLOOD‐FP hydrodynamic model. We performed two proof‐of‐concept experiments using synthetically generated SWOT measurements. The experiments demonstrated that bathymetric depth and slope can be estimated to within 3.0 microradians or 50 cm, respectively, using SWOT WSE measurements, within the context of our DA and modeling framework. We found that channel bathymetry estimation accuracy is relatively insensitive to SWOT measurement error, because uncertainty in LISFLOOD‐FP inputs (such as channel roughness and upstream boundary conditions) is likely to be of greater magnitude than measurement error.