Vibrationally excited levels of the H2O molecule are currently detected in various environments of the interstellar medium (ISM), and collisional data for H2O, including vibration with the main colliders of the ISM, are needed. The present study focuses on the bending relaxation of H2O by collision with H when taking bending-rotation coupling explicitly into account with the rigid-bender close-coupling (RB-CC) method. With this aim, a new four-dimensional potential energy surface including the H2O bending mode is developed from a large grid of ab initio energies computed using a high level of theory. For purely rotational transitions, our RB-CC rates show very good agreement with rigid-rotor calculations performed using our new potential energy surface (PES) and with those available in the literature. Calculations for pure rotational transitions inside the excited bending level ν2 = 1 of H2O are performed and compared with their equivalents inside ν2 = 0. Vibrational quenching of H2O is also calculated and found to be much more efficient through collision with H rather than with He.