This paper presents a model for the unsteady transport of a dopant during the vertical Bridgman crystal growth process with a planar crystal-melt interface and with an axial magnetic field, and investigates the effects of varying different process variables on the crystal composition. The convective mass transport due to the buoyant convection in the melt produces nonuniformities in the concentration in both the melt and the crystal. The convective mass transport plays an important role for all magnetic field strengths considered. Diffusive mass transport begins to dominate for a magnetic flux density of 4 T and a fast growth rate, producing crystals which have an axial variation of the radially averaged crystal composition approaching that of the diffusion-controlled limit. Dopant distributions for several different combinations of process parameters are presented.