The energies and widths of several D(0) meson bound states for different nuclei are obtained using a D-meson selfenergy in the nuclear medium, which is evaluated in a selfconsistent manner using techniques of unitarized coupled-channel theory. The kernel of the meson-baryon interaction is based on a model that treats heavy pseudoscalar and heavy vector mesons on equal footing, as required by heavy quark symmetry. We find D(0) bound states in all studied nuclei, from (12)C up to (208)Pb. The inclusion of vector mesons is the keystone for obtaining an attractive D-nucleus interaction that leads to the existence of D(0)-nucleus bound states, as compared to previous studies based on SU(4) flavor symmetry. In some cases, the half widths are smaller than the separation of the levels, what makes possible their experimental observation by means of a nuclear reaction. This can be of particular interest for the future PANDA@FAIR physics program. We also find a D(+) bound state in (12)C, but it is too broad and will have a significant overlap with the energies of the continuum.