Four new compounds, RbSiBiS(4), RbGeBiS(4), CsSiBiS(4), and CsGeBiS(4), have been synthesized by means of the reactive flux method. The isostructural compounds RbSiBiS(4), RbGeBiS(4), and CsGeBiS(4) crystallize in space group P2(1)/c of the monoclinic system with four formula units in cells of dimensions at 153 K of a = 6.4714(4) A, b = 6.7999(4) A, c = 17.9058(11) A, and beta = 108.856(1) degrees for RbSiBiS(4), a = 6.5864(4) A, b = 6.8559(4) A, c = 17.9810(12) A, and beta = 109.075(1) degrees for RbGeBiS(4), and a = 6.5474(4) A, b = 6.9282(4) A, c = 18.8875(11) A, and beta = 110.173(1) degrees for CsGeBiS(4). CsSiBiS(4) crystallizes in a different structure type in space group P2(1)/c of the monoclinic system with four formula units in a cell of dimensions at 153 K of a = 9.3351(7) A, b = 6.9313(5) A, c = 12.8115(10) A, and beta = 109.096(1) degrees. The two structure types are closely related and consist of [MBiS(4)(-)] (M = Si, Ge) layers separated by bicapped trigonal-prismatically coordinated alkali-metal atoms. In each, the M atom is coordinated to a tetrahedron of four S atoms and the Bi atom is coordinated to seven S atoms comprising five close S atoms at the corners of a square pyramid with Bi near the center of the basal plane and the sixth and seventh S atoms further away to complete a distorted monocapped trigonal prism. The optical band gaps of 2.23 eV for RbGeBiS(4) and 2.28 eV for CsGeBiS(4) were deduced from their diffuse reflectance spectra. From a band structure calculation, the optical absorption for RbGeBiS(4) originates from the [GeBiS(4)(-)] layer. The Ge 4p orbitals, Bi 6p orbitals, and S 3p orbitals are highly hybridized.