Abstract The control of Bi incorporation and material properties in III-V-Bi alloys has proved challenging due to their high sensitivity to the epitaxial growth parameters. Here, we present a methodology for determining the variation in the Ga, As, and Bi fluxes and the temperature across a stationary substrate in molecular beam epitaxy. By correlating the flux distributions with material properties, we identify distinct regimes for epitaxy of GaAsBi. In particular, we devise a detailed image of the interplay between Bi incorporation and structural properties of a bulk GaAs0.96Bi0.04 layer grown on GaAs(1 0 0) with respect to the As/Ga ratio. The influence of As/Ga is analyzed with high resolution over the important stoichiometric range (i.e. As/Ga = 0.6–1.6). Growth outside the near-stoichiometric As/Ga regime leads to decreased Bi incorporation, decreased structural quality and the formation of Ga, Ga/Bi or Bi droplets. On the other hand, growth at As/Ga = 1.00–1.17 leads to maximized material quality. For this regime, the surface roughness is further optimized by fine-tuning the As/Ga ratio to suppress surface mounding to a value of 0.5 nm. The results reveal the extreme sensitivity of GaAsBi growth to small variations in the As/Ga ratio, and demonstrate the applicability of stationary growth in studying these effects.