The successful growth of Bi epilayers, and for the first time Bi-CdTe superlattices, by molecular-beam epitaxy (MBE) on CdTe (111)B substrates is reported. X-ray diffraction shows several orders of satellites indicative of the abruptness of the interfaces. Initial analysis by high-resolution transmission electron microscopy shows sharp interfaces, although stacking faults are evident in the growth of CdTe on Bi. The growth of Bi layers exhibits streaked reflection high-energy electron diffraction patterns with clear Kikuchi lines. This is the first direct evidence for the layer by layer growth of Bi on CdTe by MBE. A detailed characterization of the electron and hole densities and mobilities in epilayers with a range of thicknesses has been obtained from a hybrid mixed conduction analysis of the magneto-transport data. Temperature dependences of the minority electron concentrations at greater-than-or-equal-to 150 K have yielded the first convincing evidence for a semimetal to semiconductor transition in Bi thin films, at a thickness between 200 and 300 angstrom.