This work aims to study the radiation shielding properties of Bi2O3–B2O3 –SiO2–Na2O glasses (coded as BBS-glasses) using the Geant4 simulation and to determine the effect of the Bi2O3 content on the attenuation capability of the glasses. The mass attenuation coefficient (MAC) of BBS-glasses was estimated by the Monte Carlo simulations in Geant4, and the simulated results were validated by XCOM software. The maximum relative difference between the two approaches throughout the considered gamma-ray energies was 1.05, 1.20, 1.40, 1.52, 1.21, and 1.5%, respectively, for BBS-0–BBS-5, which means that MAC estimated through the Geant4 simulation and XCOM are in good agreement; hence, the simulation results are accurate. At each investigated energy, the linear attenuation coefficient value increases with Bi2O3 as a result of the higher molecular weight of Bi2O3, hence higher electron–photon interactions. The effective atomic number varies from 7.65–9.37, 19.64–66.66, 29.01–73.92, 36.54–76.76, 42.72–78.29, and 47.89–79.23 for BBS-0–BBS-5, respectively. The half value layer for the selected glasses followed the trend: (HVL)BBS-5 < (HVL)BBS-4 < (HVL)BBS-3 < (HVL)BBS-2 < (HVL)BBS-1 < (HVL)BBS-0. The transmission factor reduces as the thickness of the glasses increases, and the Bi2O3 content in the glasses greatly improved their photon shielding and protection ability. The comparison between the mean free path of the selected glasses with other materials revealed that BBS-5 is a better photon shield than BC and RS-360 commercial glass shields.