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We develop the realistic minimal electronic model for recently discovered BiS _2 superconductors including the spin–orbit (SO) coupling based on the first-principles band structure calculations. Due to strong SO coupling, characteristic for the Bi-based systems, the tight-binding low-energy model necessarily includes p _x , p _y , and p _z orbitals. We analyze a potential Cooper-pairing instability from purely repulsive interaction for the moderate electronic correlations using the so-called leading angular harmonics approximation. For small and intermediate doping concentrations we find the dominant instabilities to be ${d}_{{x}^{2}-{y}^{2}}$ -wave, and s _± -wave symmetries, respectively. At the same time, in the absence of the sizable spin fluctuations the intra and interband Coulomb repulsions are of the same strength, which yield the strongly anisotropic behavior of the superconducting gaps on the Fermi surface. This agrees with recent angle resolved photoemission spectroscopy findings. In addition, we find that the Fermi surface topology for BiS _2 layered systems at large electron doping can resemble the doped iron-based pnictide superconductors with electron and hole Fermi surfaces maintaining sufficient nesting between them. This could provide further boost to increase T _c in these systems.