Recently, significant attention has been devoted to exploring the large bandgap bowing and spin-orbit splitting in GaBixAs1-x. alloys. We attribute the origins of these effects to a restructuring of the alloy valence band induced by an anticrossing interaction between the delocalized GaAs p-like states and the resonant localized Bi p-like states. Hybridization of like-symmetry states leads to the splitting of the heavy hole, light hole and spin-orbit split-off bands into sets of E+ and E- subbands. The splitting is confirmed experimentally by photomodulated reflectance spectroscopy in alloys with Bi concentrations up to x = 0.084. The bandgap bowing is a direct consequence of the strong upward shift of the uppermost heavy and light hole E+ bands with increasing Bi concentration, while the much slower ascent of the spin-orbit split-off E+ band produces the large rise in the spin-orbit splitting energy.