Escherichia coli in shear flow near a surface are shown to exhibit a steady propensity to swim towards the left (within the relative coordinate system) of that surface. This phenomenon depends solely on the local shear rate on the surface, and leads to cells eventually aligning and swimming upstream preferentially along a left sidewall or crevice in a wide range of flow conditions. The results indicate that flow-assisted translation and upstream swimming along surfaces might be relevant in various models of bacterial transport, such as in pyelonephritis and bacterial migration in wet soil and aquatic environments in general.