Among solution-processed nanocrystals containing environmentally benign elements, bismuth sulfide (Bi2S3) is a very promising n-type semiconductor for solar energy conversion. Despite the prompt success in the fabrication of optoelectronic devices deploying Bi2S3 nanocrystals, the limited understanding of electronic properties represents a hurdle for further materials developments. Here, two key materials science issues for light-energy conversion are addressed: bandgap tunability via the quantum size effect, and photocarrier trapping. Nanocrystals are synthesized with controlled sizes varying from 3 to 30 nm. In this size range, bandgap tunability is found to be very small, a few tens of meV. First principles calculations show that a useful blueshift, in the range of hundreds of meV, is achieved in ultra-small nanocrystals, below 1.5 nm in size. Similar conclusions are envisaged for the class of pnictide chalcogenides with a ribbon-like structure [Pn4Ch6]n (Pn = Bi, Sb; Ch = S, Se). Time-resolved differential transmission spectroscopy demonstrates that only photoexcited holes are quickly captured by intragap states. Photoexcitation dynamics are consistent with the scenario emerging in other metal-chalcogenide nanocrystals: traps are created in metal-rich nanocrystal surfaces by incomplete passivation by long fatty acid ligands. In large nanocrystals, a lower bound to surface trap density of one trap every sixteen Bi2S3 units is found.