Microswimmers such as E. coli bacteria accumulate and exhibit an intriguing dynamics near walls, governed by hydrodynamic and steric interactions. Insight into the underlying mechanisms and predominant interactions demand a detailed characterization of the entrapment process. We employ a mesoscale hydrodynamics simulation approach to study entrapment of an E. coli-type cell at a no-slip wall. The cell is modeled by a spherocylindrical body with several explicit helical flagella. Three stages of the entrapment process can be distinguished: the approaching regime, where a cell swims toward a wall on a nearly straight trajectory; a scattering regime, where the cell touches the wall and reorients; and a surface-swimming regime. Our simulations show that steric interactions may dominate the entrapment process, yet, hydrodynamic interactions slow down the adsorption dynamics close to the boundary and imply a circular motion on the wall. The locomotion of the cell is characterized by a strong wobbling dynamics, with cells preferentially pointing toward the wall during surface swimming.