Gamma-rays and fast and thermal neutron attenuation features of (Bi2O3)(x)-(TeO2)((100-x)) (where x = 5, 8, 10, 12, and 15 mol%) and [(TeO2)(0.7)-(B2O3)(0.3)]((1-x))-(Bi2O3)(x) (where x = 0.05, 0.10, 0,15, 0.20, 0.25, and 0.3 mol%) glass systems have been explored and compared. For all samples, mass attenuation coefficients (mu/rho) are estimated within 0.015-15 MeV photon energy range by MCNP5 simulation code and correlated with WinXCom results, which showed a satisfactory agreement between computed mu/rho values by these both methods. Additionally, effective atomic number (Z(eff)), effective electron density (N-eff), half-value layer (HVL), tenth-value layer (TVL), mean free path (MFP), total atomic cross-section (sigma(a)), and total electronic cross-section (sigma(e)) are calculated by utilizing mu/rho values. The mu/rho, Z(eff), and N-eff are energy dependent and have higher values at the lowest energy and smaller values at higher energies. Moreover, using the G-P fitting method as a function of penetration depth (up to 40 mfp) and incident photon energy (0.015-15 MeV range), exposure buildup factors (EBFs) and energy absorption buildup factors (EABFs) are evaluated. Both 85TeO(2)-15Bi(2)O(3) (mol%) and 49TeO(2)-21B(2)O(3)-30Bi(2)O(3) (mol%) samples, by possessing higher values of Z(eff), exhibit minimum EBF and EABF values. Highest mu/rho, Z(eff) values and lowest HVL, TVL, MFP values of 49TeO(2)-21B(2)O(3)-30Bi(2)O(3) (mol%) sample indicated its better gamma-ray absorption capability among all selected glasses. Further, macroscopic effective removal cross-section for fast neutrons (sigma(R)), coherent scattering cross-section (sigma(cs)), incoherent scattering cross-section (sigma(ics)), absorption cross-section (sigma(A)), and total cross-section (sigma(T)) values for thermal neutron attenuation have been computed. Among all samples, 49TeO(2)-21B(2)O(3)-30Bi(2)O(3) (mol%) glass possesses a better sigma(R) value for fast neutron attenuation, while the largest 'sigma(T)' value of 66.5TeO(2)-28.5B(2)O(3)-5Bi(2)O(3) (mol%) sample suggests its good thermal neutron absorption efficiency.