High room-temperature electron mobility and optical transparency in the visible spectrum distinguishes BaSnO3 from other perovskite oxides. The origin of low mobility in thin films as compared to their bulk counterpart is attributed to the presence of dislocations in films with nearly no discussion on the role of point defects such as cation non-stoichiometry. Using high-resolution X-ray diffraction, Rutherford backscattering spectrometry, thermal, and electronic transport measurements, we show that a growth window, in which cation stoichiometry is self-regulating, can be achieved for BaSnO3 films on SrTiO3(001) and (La0.3Sr0.7)(Al0.65Ta0.35)O3(001) (LSAT) substrates using a hybrid molecular beam epitaxy approach. BaSnO3 films on SrTiO3 grown within the growth window yielded a mobility value of 105 cm2 V−1 s−1 at a density, 2.5 × 1020 cm−3. Bulk-like thermal conductivity of 13.3 ± 1.46 W m−1 K−1 was achieved for stoichiometric films. Both Ba- and Sn-deficient films resulted into charge compensation and low mobility, with a stronger dependence for Sn-deficient films.