We report on the synthesis, crystal structures, optoelectronic properties and solar cell device studies of three novel organic-inorganic iodobismuthates - [C3H4NS]3[Bi2I9] ([TH]3[Bi2I9]), [C3H4N2]3[Bi2I9] ([IM]3[Bi2I9]) and [C3H5N2S][BiI4] ([AT][BiI4]) as lead-free light harvesters. [TH]3[Bi2I9] and [IM]3[Bi2I9] show zero-dimensional structures, whereas a one-dimensional edge-sharing chain structure of BiI6-octahedra was observed in [AT][BiI4], with interchain short II contacts also giving rise to the possibility of three-dimensional charge transport ability. Accordingly, greater energy dispersion in the band structure of [AT][BiI4] can be observed, and less contribution from the organic moities at the conduction band minimum in [AT][BiI4] than [TH]3[Bi2I9] have been confirmed by density functional theory calculations. Moreover, bandgap values are redshifted from 2.08 eV for [TH]3[Bi2I9] and 2.00 eV for [IM]3[Bi2I9] to 1.78 eV for [AT][BiI4], determined by UV-Vis reflectance spectroscopy. Power conversion efficiency of 0.47% has been achieved by using ([AT][BiI4]) as the light absorber in a hole-conductor-free, fully printable solar cell, with relatively good reproducibility. We also note the observation of a capacitance effect for the first time in a photovoltaic device with bismuth-based solar absorber, which may be related to the mesoporous carbon counter-electrode.