Although the relevant properties of the bismuthinite \({Bi}_{2}{S}_{3}\), it was recently approved that the substitution of Se atoms in the \({Bi}_{2}{S}_{3}\) lattice can significantly enhance its electro-optical properties. In the present work, a detailed study on the structural, electronic and optical properties of \({Bi}_{2}{S}_{2.75}{Se}_{0.25}\) has been carried out based on first principle calculations. The simultaneous effect of Se-doping and spin-orbit coupling (SOC) on bismuth sulfide \({Bi}_{2}{S}_{3}\) was investigated. Our calculations show that \({Bi}_{2}{S}_{2.75}{Se}_{0.25}\) exhibits a narrow direct band gap of 1.062 eV after inclusion of the (SOC). The calculation of the carrier effective masses indicates that \({Bi}_{2}{S}_{2.75}{Se}_{0.25}\) may possess a high electron mobility material which is in accordance with experimental studies. The linear absorption optical spectra for both \({Bi}_{2}{S}_{3}\) and \({Bi}_{2}{S}_{2.75}{Se}_{0.25}\)show that doping bismuthinite with (Se) increases the optical absorption coefficient in the visible range and takes a value up to \(10 {10}^{5}{cm}^{-1}\). In addition, the dielectric function, optical conductivity and the energy loss function of \({Bi}_{2}{S}_{3}\) and \({Bi}_{2}{S}_{2.75}{Se}_{0.25}\)were also derived. The addition of the (Se) content induces a red shift in agreement with experimental studies. A noticeable effect of the (SOC) on the linear optical parameters was observed. The stability of the excitons was also studied by the estimation of the binding energy value. The dispersion energy parameters of \({Bi}_{2}{S}_{3}\) and \({Bi}_{2}{S}_{2.75}{Se}_{0.25}\)were estimated using a single oscillator model. Some nonlinearities have been computed with and without inclusion of (SOC) showing that \({Bi}_{2}{S}_{2.75}{Se}_{0.25}\)with large nonlinear optical parameters is promising candidate in photonic switching applications.