A one-electron model potential approach for calculating the binding energies of an excess electron interacting with water clusters is presented. Drude oscillators are employed on the water monomers to describe electron-water polarization and dispersion interactions. It is demonstrated that the resulting model gives electron binding energies very close to the predictions of ab initio CCSD(T) calculations. Dispersion interactions and high-order renormalization effects are found to make large contributions to the electron binding energies.