We demonstrate the controlled growth of Bi(110) and Bi(111) films on an α-Al2O3(0001) substrate by surface x-ray diffraction and x-ray reflectivity using synchrotron radiation. At temperatures as low as 40 K, unanticipated pseudo-cubic Bi(110) films are grown with thicknesses ranging from a few to tens of nanometers. The roughness at the film-vacuum as well as the film-substrate interface, can be reduced by mild heating, where a crystallographic orientation transition of Bi(110) towards Bi(111) is observed at 400 K. From 450 K onwards high quality ultrasmooth Bi(111) films form. Growth around the transition temperature results in the growth of competing Bi(110) and Bi(111) domains.