We have measured the quasi-elastic neutron scattering (QENS) of an electrohydrodynamic liquid bridge formed between two beakers of pure water when a high voltage is applied, a setup allowing to investigate water under high-voltage without high currents. From this experiment two proton populations were distinguished: one consisting of protons strongly bound to oxygen atoms (immobile population, elastic component) and a second one of quasi-free protons (mobile population, inelastic component) both detected by QENS. The diffusion coefficient of the quasi-free protons was found to be D = (26 +/- 10) x 10(-5) cm(2) s(-1) with a jump length l(av) similar to 3 angstrom and an average residence time of tau(0) = 0.55 +/- 0.08 ps. The associated proton mobility in the proton channel of the bridge is similar to 9.34 x 10(-7) m(2) V-1 s(-1), twice as fast as diffusion-based proton mobility in bulk water. It also matches the so-called electrohydrodynamic or "apparent" charge mobility, an experimental quantity which so far has lacked molecular interpretation. These results further corroborate the proton channel model for liquid water under high voltage and give new insights into the molecular mechanisms behind electrohydrodynamic charge transport phenomena and delocalization of protons in liquid water.