  We present a simple model for bacteria like \emph{Escherichia coli} swimming
near solid surfaces. It consists of two spheres of different radii connected by
a dragless rod. The effect of the flagella is taken into account by imposing a
force on the tail sphere and opposite torques exerted by the rod over the
spheres. The hydrodynamic forces and torques on the spheres are computed by
considering separately the interaction of a single sphere with the surface and
with the flow produced by the other sphere. Numerically, we solve the linear
system which contains the geometrical constraints and the force-free and
torque-free conditions. The dynamics of this swimmer near a solid boundary is
very rich, showing three different behaviors depending on the initial
conditions: (1) swimming in circles in contact with the wall, (2) swimming in
circles at a finite distance from the wall, and (3) swimming away from it.
Furthermore, the order of magnitude of the radius of curvature for the circular
motion is in the range $8-50\,\mu$m, close to values observed experimentally.
