For ion-water clusters, the use of a suitable embedding potential within the MBE subsystem calculations out to be essential. Here, we compared the use of a point-charge embedding potential (with parametrized partial charges) as well as frozen-density embedding with the unrelaxed monomer frozen densities (FDE) and with monomer densities relaxed in freeze-and-thaw cycles (FDE-ft). While we notice that for the db-MBE the resulting energies are less sensitive to the choice of the embedding potential than for the eb-MBE, we still find that in all cases, FDE-ft embedding leads to the most accurate results. Thus, we recommend to use FDE-ft embedding, which does not rely on any parametrization, in future applications of the db-MBE to systems with large polarization effects.