Nuclear radiation shielding capabilities for a glass series 20Bi2O3 - xPbO - (80 - 2x)B2O3 - xGeO2 (where x = 5, 10, 20, and 30 mol%) have been investigated using the Phy-X/PSD software and Monte Carlo N-Particle transport code. The mass attenuation coefficients (μm) of selected samples have been estimated through XCOM dependent Phy-X/PSD program and MCNP-5 code in the photon-energy range 0.015-15 MeV. So obtained μm values are used to calculate other γ-ray shielding parameters such as half-value layer (HVL), mean-free-path (MFP), etc. The calculated μm values were found to be 71.20 cm2/g, 76.03 cm2/g, 84.24 cm2/g, and 90.94 cm2/g for four glasses S1 to S4, respectively. The effective atomic number (Zeff)values vary between 69.87 and 17.11 for S1 or 75.66 and 29.11 for S4 over 0.05-15 MeV of photon-energy. Sample S4, which has a larger PbO/GeO2 of 30 mol% in the bismuth-borate glass, possesses the lowest MFP and HVL, providing higher radiation protection efficiency compared to all other combinations. It shows outperformance while compared the calculated parameters (HVL and MFP) with the commercial shielding glasses, different alloys, polymers, standard shielding concretes, and ceramics. Geometric Progression (G-P) was applied for evaluating the energy absorption and exposure buildup factors at energies 0.015-15 MeV with penetration depths up to 40 mfp. The buildup factors showed dependence on the MFP and photon-energy as well. The studied samples' neutron shielding behavior was also evaluated by calculating the fast neutron removal cross-section (ΣR), i.e. found to be 0.139 cm-1 for S1, 0.133 cm-1 for S2, 0.128 cm-1 for S3, and 0.12 cm-1 for S4. The results reveal a great potential for using a glass composite sample S4 in radiation protection applications.