The simple cubic perovskite crystal structure of superconducting (Rb,Ba)BiO3 makes it an ideal system for the study of perovskite heteroepitaxy. We report novel growth phenomena which have been observed in (Rb,Ba)BiO3 films grown by molecular beam epitaxy (MBE). For growth on MgO, the orientation of the film is observed to depend on the substrate temperature during growth, changing from (1 1 0) to (1 0 0) with increasing temperature. For films on SrTiO3, the large (10%) lattice mismatch appears to cause small grain rotations, resulting in a film with many low angle grain boundaries. In at least one growth regime, (2 2 1) oriented grains nucleate and grow on Ʃ3 coincidence boundaries on a faceted (1 0 0) oriented film.