The past decade has witnessed the rapid introduction of organic-inorganic hybrid compounds in photovoltaic applications. Motivated by the strong demand for stable and non-toxic materials in this class, we report a theoretical study on the structural, thermodynamic, electronic and dielectric properties of alkali-metal-based bismuth ternary chalcogenides. In particular, we employ state-of- the-art density functional theory (DFT) to explore the potential of ABiX2 and ABiX3 (A = Na, K and X = O, S) as light-absorbing media. All the compounds under consideration were found to be thermodynamically and mechanically stable. These materials are found to be all semiconductors with Kohn-Sham band gaps ranging between 0.80 eV and 1.80 eV. Although all but NaBiO2 and KBiO2 are indirect band-gap semiconductors, the onset of the imaginary part of their dielectric functions, the optical gap, is only marginally larger than the quasi-particle gap. This is due to the generally flat nature of both the conduction and the valence bands. Given the notorious underes- timation of the band gap from semi-local DFT functionals, we expect these compounds to absorb light in the upper part of the visible spectrum. In all cases the valence band is dominated by O- and S-p orbitals and the conduction one by Bi-p, suggesting the possibility of excitons with low binding energy. The only exceptions are NaBiO2 and KBiO2 for which the O-p states dominate the density of states at both sides of the band gap.