Newly discovered Bi-O-S compounds remain an enigma in attempts to understand their electronic properties. A recent study of Bi4O4S3 has shown it to be a mixture of two phases, Bi2OS2 and Bi3O2S3, the latter being superconducting (Phelan et al 2013 J. Am. Chem. Soc. 135 5372-4). Using density functional theory, we explore the electronic structure of both the phases and the effect of the introduction of extra BiS2 bilayers. Our results demonstrate that the S2 layers dope the bismuth-sulphur bands and this causes metallisation. The bands at the Fermi level are of clear two-dimensional character. One band manifold is confined to the two adjacent, square-lattice bismuth-sulphur planes, a second manifold is confined to the square lattice of sulphur dimers. We show that the introduction of extra BiS2 bilayers does not influence the electronic structure. Finally, we also show that spin-orbit coupling does not have any significant effect on the states close to the Fermi level at the energy scale considered.