Ultrathin films of Na3Bi on insulating substrates are desired for opening a bulk band gap and generating the quantum spin Hall effect from a topological Dirac semimetal, though continuous films in the few nanometer regime have been difficult to realize. Here, we utilize alternating layer molecular beam epitaxy (MBE) to achieve uniform and continuous single crystal films of Na3Bi(0001) on insulating Al2O3(0001) substrates and demonstrate electrical transport on films with 3.8 nm thickness (4 unit cells). The high material quality is confirmed through in situ reflection high-energy electron diffraction (RHEED), scanning tunneling microscopy (STM), x-ray diffraction (XRD), and x-ray photoelectron spectroscopy (XPS). In addition, these films are employed as seed layers for subsequent growth by codeposition, leading to atomic layer-by-layer growth as indicated by RHEED intensity oscillations. These material advances facilitate the pursuit of quantum phenomena in thin films of Dirac semimetals.