The gamma shielding and dosimetric quantities of the optical (55-x)B2O3 − 20CaF2- 5GeO2- 20Bi2O3-xCuO glass system are reported here. We studied different concentrations of CuO content, that is, 0 (BCGBC1), 1 (BCGBC2), 3 (BCGBC3), and 5 (BCGBC4) mol%. The mass attenuation coefficient of the glass system was estimated for 15 – 15,000 keV photons through the use of XCOM. Other photon shielding and dosimetric quantities such as mass energy absorption coefficient μen, specific gamma ray constant Γ, equivalent atomic number Zeq, effective atomic number Zeff, effective electron density Neff, gamma dose rate Dr and gamma photon buildup factors (exposure (EBF) and energy absorption (EABF) are estimated using standard deterministic expressions. Analysis of other related photon absorption quantities shows that there is a thin line between the gamma shielding ability of the glasses especially at energies beyond 0.1 MeV. In addition, the increase in the CuO content of the glasses slightly decreased the photon buildup within the glasses. The potential of the glasses to function well in radiation protective relation applications was demonstrated by the higher mass attenuation coefficient of BCGBC4 glass compared to different commercial shielding glasses, concrete samples, and other categories of materials with high shielding functionality.