Glass samples were synthesized according to 10Li₂O + 20CuO + xBi₂O₃ + (70 − x)B₂O₃, where x = 0, 10, 20, 30, 40 mol% by the melt-quenching method. The ability of the prepared glass to protect against gamma rays and neutrons was examined experimentally and theoretically. The mass attenuation coefficient (MAC) was calculated experimentally at energies of 0.662, 1.173, and 1.333 MeV using ¹³⁷Cs and ⁶⁰Co sources. The obtained results were compared with the theoretical ones using a Phy-x/PSD software program version 0.1.0.0. It was found that the experimental and theoretical results are very agreed upon. Moreover, other nuclear radiation shielding parameters were evaluated. The results showed that the addition of bismuth oxide leads to an improvement in the ability of the composite glass to attenuate gamma rays by increasing the values of MAC and Z_eff, while it led to a decrease in the HVL and MFP, as well as the EBF and EABF. The results also showed that the addition of copper oxide led to an improvement in the ability of the present glass to slow down fast neutrons. Sample BiS40 showed the best result for gamma ray attenuation and sample BiS10 gave the best result for fast neutron removal cross section. The results were compared with some materials used for gamma ray shielding and fast neutron removal cross section, and it was concluded that samples Bi40 and BiS10 outperformed all commercial materials.