The electronic structure of bulk GaAs$_{1-x}$Bi$_x$ systems for different atomic configurations and Bi concentrations is calculated using density functional theory. The results show a Bi-induced splitting between the light-hole and heavy-hole bands at the $Gamma$-point. We find a good agreement between our calculated splittings and experimental data. The magnitude of the splitting strongly depends on the local arrangement of the Bi atoms but not on the uni-directional lattice constant of the supercell. The additional influence of external strain due to epitaxial growth on GaAs substrates is studied by fixing the in-plane lattice constants.
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