We conduct high-resolution collisionless N-body simulations to investigate the tidal evolution of dwarf galaxies on an eccentric orbit in the Milky Way (MW) potential. The dwarfs originally consist of a low surface brightness stellar disc embedded in a cosmologically motivated dark matter halo. During 10 Gyr of dynamical evolution and after five pericentre passages, the dwarfs suffer substantial mass loss and their stellar component undergoes a major morphological transformation from a disc to a bar and finally to a spheroid. The bar is preserved for most of the time as the angular momentum is transferred outside the galaxy. A dwarf spheroidal (dSph) galaxy is formed via gradual shortening of the bar. This work thus provides a comprehensive quantitative explanation of a potentially crucial morphological transformation mechanism for dwarf galaxies that operates in groups as well as in clusters. We compare three cases with different initial inclinations of the disc and find that the evolution is fastest when the disc is coplanar with the orbit. Despite the strong tidal perturbations and mass loss, the dwarfs remain dark matter dominated. For most of the time, the one-dimensional stellar velocity dispersion, σ, follows the maximum circular velocity, V_max, and they are both good tracers of the bound mass. Specifically, we find that M_bound ~ V^3.5_max and in agreement with earlier studies based on pure dark matter simulations. The latter relation is based on directly measuring the stellar kinematics of the simulated dwarf, and may thus be reliably used to map the observed stellar velocity dispersions of dSphs to halo circular velocities when addressing the missing satellites problem.