Silver bismuth-iodides (AgxBiyIx+3y) are a promising class of materials with potential for use as absorber layers in optoelectronic devices, but theoretical investigations into their properties are hindered by their large degree of site-disorder and unique layered structures. Here, we demonstrate a cluster-based description of the total energy that, paired with a simulated annealing minimizer, can create low-energy atomic models of AgxBiyIx+3y from a pool of over 10100 possible choices. We employ first principles density functional theory to calculate band gaps, densities of states, effective masses, and absorption spectra of the ground state structures. Lattice constants, band gaps, and optical spectra of the structures compare favorably with available experimental results. This work additionally provides new insights into the physical and electronic structure of the more complicated Ag-Bi-I stoichiometries. The models generated can be used to gain insight on the role of various defects on the growth and properties of these materials.