© 2015 American Physical Society. We investigate the molecular beam epitaxy (MBE) growth of GaAs1-xBix film using density functional theory with spin-orbit coupling to understand the growth of this film, especially the mechanisms of Bi incorporation. We study the stable adsorption structures and kinetics of the incident molecules (As2 molecule, Ga atom, Bi atom, and Bi2 molecule) on the (2×1)-Gasub||Bi surface and a proposed q(1×1)-Gasub||AsAs surface, where Gasub||XY refers to a Ga-terminated GaAs(001) substrate with surface layers of X and Y. The q(1×1)-Gasub||AsAs surface has a quasi-(1×1) As layer above the Ga-terminated GaAs substrate and a randomly oriented As dimer layer on top. We obtain the desorption and diffusion barriers of the adsorbed molecules and also the reaction barriers of three key processes related to Bi evolution, namely, Bi incorporation, As/Bi exchange, and Bi clustering. The results help explain the experimentally observed dependence of Bi incorporation on the As/Ga ratio and growth temperature. Furthermore, we find that As2 exchange with Bi of the (2×1)-Gasub||Bi surface is a key step controlling the kinetics of the Bi incorporation. Finally, we explore two possible methods to enhance the Bi incorporation, namely, replacing the MBE growth mode from codeposition of all fluxes with a sequential deposition of fluxes and applying asymmetric in-plane strain to the substrate.