Escherichia coli exhibit both shear-stabilized rolling and a transition to stationary adhesion while adhering in fluid flow. Understanding the mechanism by which this shear-enhanced adhesion occurs is an important step in understanding bacterial pathogenesis. In this work, simulations are used to investigate the relative contributions of fimbrial deformation and bond transitions to the rolling and stationary adhesion of E. coli. Each E. coli body is surrounded by many long, thin fimbriae terminating in a single FimH receptor that is capable of forming a catch bond with mannose. As simulated cells progress along a mannosylated surface under flow, the fimbriae bend and buckle as they interact with the surface, and FimH-mannose bonds form and break according to a two-state, allosteric catch-bond model. In simulations, shear-stabilized rolling resulted from an increase in the low-affinity bond number due to increased fimbrial deformation with shear. Catch-bond formation did not occur during cell rolling, but instead led to the transition to stationary adhesion. In contrast, in leukocyte and platelet systems, catch bonds appear to be involved in the stabilization of rolling, and integrin activation is required for stationary adhesion.