The salt bridge formation and stability in the terminated lysine-glutamate dipeptide is investigated in water clusters of increasing size up to the limit of bulk water. Proton transfer dynamics between the acidic and basic side chains is described by DFT-based Born-Oppenheimer molecular dynamics simulations. While the desolvated peptide prefers to be in its neutral state, already the addition of a single water molecule can trigger proton transfer from the glutamate side chain to the lysine side chain, leading to a zwitterionic salt bridge state. Upon adding more water molecules we find that stabilization of the zwitterionic state critically depends on the number of hydrogen bonds between side chain termini, the water molecules, and the peptidic backbone. Employing classical molecular dynamics simulations for larger clusters, we observed that the salt bridge is weakened upon additional hydration. Consequently, long-lived solvent shared ion pairs are observed for about 30 water molecules while solvent separated ion pairs are found when at least 40 or more water molecules hydrate the dipeptide. These results have implications for the formation and stability of salt bridges at partially dehydrated surfaces of aqueous proteins.