For both the B2O3-Bi2O3-CaO and B2O3-Bi2O3-SrO glass systems, γ-ray and neutron attenuation qualities were evaluated. Utilizing the Phy-X/PSD program, within the 0.015–15 MeV energy range, linear attenuation coefficients (µ) and mass attenuation coefficients (μ/ρ) were calculated, and the attained μ/ρ quantities match well with respective simulation results computed by MCNPX, Geant4, and Penelope codes. Instead of B2O3/CaO or B2O3/SrO, the Bi2O3 addition causes improved γ-ray shielding competence, i.e., rise in effective atomic number (Zeff) and a fall in half-value layer (HVL), tenth-value layer (TVL), and mean free path (MFP). Exposure buildup factors (EBFs) and energy absorption buildup factors (EABFs) were derived using a geometric progression (G–P) fitting approach at 1–40 mfp penetration depths (PDs), within the 0.015–15 MeV range. Computed radiation protection efficiency (RPE) values confirm their excellent capacity for lower energy photons shielding. Comparably greater density (7.59 g/cm3), larger μ, μ/ρ, Zeff, equivalent atomic number (Zeq), and RPE, with the lowest HVL, TVL, MFP, EBFs, and EABFs derived for 30B2O3-60Bi2O3-10SrO (mol%) glass suggest it as an excellent γ-ray attenuator. Additionally, 30B2O3-60Bi2O3-10SrO (mol%) glass holds a commensurably bigger macroscopic removal cross-section for fast neutrons (ΣR) (=0.1199 cm−1), obtained by applying Phy-X/PSD for fast neutrons shielding, owing to the presence of larger wt% of ‘Bi’ (80.6813 wt%) and moderate ‘B’ (2.0869 wt%) elements in it. 70B2O3-5Bi2O3-25CaO (mol%) sample (B: 17.5887 wt%, Bi: 24.2855 wt%, Ca: 11.6436 wt%, and O: 46.4821 wt%) shows high potentiality for thermal or slow neutrons and intermediate energy neutrons capture or absorption due to comprised high wt% of ‘B’ element in it.