Biological systems have been shown to shuttle excess protons long distances by taking advantage of tightly organized hydrogen-bonded water bridges in hydrophobic protein cavities, and similar effects have been observed in carbon nanotubes. In this theoretical study we investigate how quantum effects of proton motion impact the rate constants for charge transfer in a model system consisting of a donor and acceptor molecule separated by a single-molecule water bridge. We calculate quantum and classical rate constants for the transfer of an excess proton over two possible paths, one with an H3O+ intermediate, and one with an OH- intermediate. Quantum effects are included through ring polymer molecular dynamics (RPMD) calculations. We observe a 4-fold enhancement of reaction rate constants due to proton tunneling at temperatures between 280 and 320 K, as shown by transmission coefficient calculations. Deuteration of the donor and acceptor proton are shown to decrease the reaction rate constant by a factor of SO, and this is another indicator that tunneling plays an important role in this proton transfer mechanism.