We investigate the bismuth (111) surface by means of time and angle resolved photoelectron spectroscopy. The parallel detection of the surface states below and above the Fermi level reveals a giant anisotropy of the spin-orbit spitting. These strong deviations from the Rashba-like coupling cannot be treated in k·p perturbation theory. Instead, first principles calculations could accurately reproduce the experimental dispersion of the electronic states. Our analysis shows that the giant anisotropy of the spin-orbit splitting is due to a large out-of plane buckling of the spin and orbital texture.