Microgravity experiments, especially materials processing experiments, have often been hampered by presence of unwanted bubbles. In this work, the effect of thermocapillary convection generated by a bubble on the Bridgman growth of a dilute binary alloy in microgravity is investigated numerically. The model is based on the quasi-steady Navier-Stokes equations for the fluid flow in the melt coupled with the conservation equations for transport of energy and species in the growth ampoule. Numerical results indicate three different growth regimes based on the distance between the bubble and the growth interface: a diffusion dominated regime that is separated from a well-mixed convection dominated regime by a transitionary region where both diffusion and bubble generated convection play an important role. In this transitionary region, the effects of bubble size and bubble location on the interface shape and the radial segregation patterns at the growth front are significant.