An analysis is outlined in which the dependence of the binding energy, E-b, stretching frequency, nu (M-A), and equilibrium bond length, r(eq), of metal-adsorbate bonds on the external interfacial field (F), and hence surface potential of relevance to electrochemical systems, are described in terms of potential-energy surface and bond-polarization parameters. Density Functional Theory (DFT) calculations for finite metal clusters with monoatomic adsorbates forming polar surface bonds are utilized both to examine metal-, adsorbate-, and field-dependent trends in the required parameters and to examine the applicability of the analytic relations in comparison with numerical calculations. To a very good approximation, the E-b-F dependence is described by the field-dependent static dipole moment, mu (S), of the metal-adsorbate bond. As expected, the field-induced changes in the potential-energy surface (PES) are determined by the r-dependent mu (S) values, i.e., the dynamic dipole moment, mu (D). The factors determining the nu (M-A)-F dependence, however, are distinctly more intricate, involving the PES anharmonicity coupled with mu (D), as well as being influenced significantly by the mu (D)-r dependence in some cases. While both mu (S) and mu (D) are influenced importantly by surface bond polarity, the role of bond polarizability appears to be quite different, so that only a crude correlation between mu (S) and mu (D) is evident. These differences further underscore the disparate nature of the E-b-F and nu (M-A)-F behavior. Nevertheless, an approximate inverse correlation between the nu (M-A)-F and r(eq)-F dependence is usually anticipated. The broad-based utility of DFT for assessing as well as predicting the role of surface bond polarization in controlling the field-dependent electrode-adsorbate PES is pointed out.