The hydration water of proteins is essential to biological activity but its properties are not yet fully understood. A recent study of dielectric relaxation of hydrated proteins [A. Levstik et al., Phys. Rev E.60 7604 (1999)] has found a behavior typical of a proton glass, with a glass transition of about 268 K. In order to analyze these results, we investigate the statistical mechanics and dynamics of a model of `two-dimensional water' which describes the hydrogen bonding scheme of bounded water molecules. We discuss the connection between the dynamics of bound water and charge transport on the protein surface as observed in the dielectric measurements.