The concentration dependence of the electrical conductance of several symmetrical electrolytes is studied using the dressed-ion transport theory (DITT) formalism. This theoretical scheme is constructed from the Fuoss-Onsager theory using the equilibrium dressed-ion theory (DIT) distribution functions for electrolyte and colloid media. The conductance equation is constructed from previous results for the relaxation of the ionic atmosphere [Varela , J. Chem. Phys. 110, 4483 (1999)], now completed with the calculation of the concentration-dependent electrophoretic velocity of ions on the basis of a DIT in a hydrodynamic point of view. Onsager's limiting law for the electrophoretic velocity based on the Debye-Huckel (DH) equilibrium distribution function is reformulated in terms of the DIT renormalized quantities, effective charges and effective screening length. The electrophoretic correction to the velocity calculated in the framework of this DITT is shown to exhibit a nontrivial dependence on the renormalized dielectric constant of the medium (epsilon*). The concentration dependence of both the deviations of the renormalized dielectric constant from the classical limit and the electrophoretic correction to the mobility is analyzed using the modified-mean spherical approximation (MMSA) value of the DIT linear response function <(alpha)over cap>(k). The behavior of epsilon* and therefore of the electrophoretic correction to the ionic (or colloidal) mobilities is studied for both the random-phase approximation (RPA) and the MMSA and they are related to ionic association through the dimensionless coupling parameter, zeta, made up from the ratio between the Bjerrum length and the mean ionic radius. The expression for the conductance of the electrolyte solutions obtained in this new theoretical approach is cast in the form of a generalized Onsager's limiting law with a concentration-dependent slope which is predicted in terms of the formation of DIT renormalized quasiparticles in the solution. Conductance predictions of several theoretical expressions for the renormalized magnitudes of electrolyte solutions are compared to direct experimental data of KCl, and are in very good agreement with the theoretical predictions of the mean-field DITT, which confirms the convenience of understanding transport processes in terms of effective dynamical entities with renormalized ionic charges interacting by means of a renormalized screened potential.