Bismuth incorporation and surface reconstruction have been studied simultaneously during GaAsBi growth by molecular beam epitaxy by means of in-situ wafer curvature monitoring and reflection high energy electron diffraction, respectively. Growth temperature and flux ratio have been varied successively. As/Ga atomic ratio close to the unity has been applied for the study of growth temperature effect. During the growth regime under the (1x3) reconstruction, Bi incorporation is found to be independent of the growth temperature, for temperatures where Bi desorption is insignificant. On the contrary, Bi incorporation becomes highly dependent on growth temperature as soon as the (2x1) reconstruction regime is reached. Only for the lower temperatures, the Bi incorporation gets to the same level during the (2x1) reconstruction than for the (1x3) reconstruction. When the As/Ga fux ratio is increased, bismuth incorporation is observed to decrease for GaAsBi growth in the (2x1) reconstruction regime. Our results indicate that the (1x3) and (2x1) surface reconstructions are always successively observed, and that an energy barrier has to overcome to transit from the (1x3) to the (2x1) reconstruction, this mechanism being temperature dependent. Finally, a difference in surface stress with reconstruction has been identified.