The dynamics of the acceleration of a short electron bunch in a strong plasma wave excited by a laser pulse in a plasma channel is studied both analytically and numerically in slab geometry. In our simulations, a fully nonlinear, relativistic hydrodynamic description for the plasma wave is combined with particle-in-cell methods for the description of the bunch. Collective self-interactions within the bunch are fully taken into account. The existence of adiabatic invariants of motion is shown to have important implications for the final beam quality. Similar to the one-dimensional case, the natural evolution of the bunch is shown to lead, under proper initial conditions, to a minimum in the relative energy spread.