We performed density functional theory calculations on heterostructures of single layers of hexagonal BN and ${\mathrm{MoS}}_{2}$ to assess the effect of doping in the BN sheet and of interstitial Na atoms on the electronic properties of the adjacent ${\mathrm{MoS}}_{2}$ layer. Our calculations predict that $n$ doping of the boron nitride subsystem by oxygen, carbon, and sulfur impurities causes noticeable charge transfer into the conduction band of the ${\mathrm{MoS}}_{2}$ sheet, while $p$ doping by beryllium and carbon leaves the molybdenum disulphide layer largely unaffected. Intercalated sodium atoms lead to a significant increase of the interlayer distance in the heterostructure and to a metallic ground state of the ${\mathrm{MoS}}_{2}$ subsystem. The presence of such $n$ dopants leads to a distinct change of valence-band and conduction-band offsets, suggesting that doped h-BN remains a suitable substrate and gate material for applications of $n$-type ${\mathrm{MoS}}_{2}$.