This research work has focused on the physical, elastic-mechanical, and shielding features of bismuth-borate glass samples consisting of varied amounts of La2O3 and Eu2O3 as additive agents to improve these characteristics. The effect of density and [La3++ Eu3+] ions mol % have been projected on the evaluated elastic moduli including Poisson's ratio and protection effectiveness against incoming γ-ray and neutron. Makishima-Mackenzie multi-components theory was employed to calculate the mechanical parameters. We found that the Vickers's microhardness and the Passion's ratio depend on both sample's density and [La3++ Eu3+] ions mol%, but follows the trend of oxygen molar volume (OMV). The mass attenuation coefficient (MAC) has been calculated in the energy range 0.015 < E < 15 MeV via XCOM, Phy-X/PSD program, and compared with Monte Carlo simulations at selected photon energies. Accordingly, other important radiation shielding parameters such as linear attenuation coefficient (LAC), transmission coefficient (TF), and radiation protection effectiveness (RPE) were calculated for the current glass systems. Also, the exposure and energy adsorption buildup factors (i.e., EBF and EABF) of the fabricated glasses were obtained. Moreover, the fast neutron removal cross section (ΣR) were evaluated and found to have the highest value of 0.11884 for the sample of [La3++ Eu3+] = 0.5. Correlation between the elastic moduli and the gamma-ray shielding features was established and explained in terms of density, molar fraction, oxygen molar volume, and oxygen packing density.