The present work reports results from systematic multiconfiguration Dirac-Hartree-Fock calculations of electronic isotope-shift factors for a set of transitions between low-lying states in neutral zinc. These electronic quantities, together with observed isotope shifts between different pairs of isotopes, provide the changes in mean-square charge radii of the atomic nuclei. Within this computational approach, different models for electron correlation are explored in a systematic way to determine a reliable computational strategy and to estimate theoretical error bars of the isotope-shift factors.