In this study, photon, neutron and charged particle shielding competences of five different glass systems which have the common chemical composition TeO2-B2O3-Bi2O3-TiO2 and contain different mole ratios of TeO2 in each sample were studied comprehensively. The fundamental photon shielding parameters, mass attenuation coefficient (mu/rho), half value layer (HVL), mean free path (MFP), effective atomic number (Z(eff) ), and electron density (N-eff ) were evaluated in the range of 0.015-20 MeV. The mu/rho values of all investigated glasses were simulated by using Geant4 Monte Carlo simulation code. Besides, the simulation work was supported utilizing the web version of XCOM code and the outcomes from two methods were compared. A good agreement between two methods was observed. Results reveal that mu/rho, MFP, HVL, Zeff and N(eff )parameters of the investigated glasses strongly depend on photon energy and chemical composition. Also, the energy absorption buildup factors (EABF) and exposure buildup factors (EBF) of the proposed glasses were calculated via G-P fitting parameters for photon energies in between 0.15 and 15 MeV. Results show that the greatest values of buildup factors take place at higher energies for all glasses. Finally, calculation of the fast neutron removal cross section (Sigma(R)) values of the glasses were performed. According to our calculations, Sigma(R) values vary between 0.1169 cm(-1) for TBBT30 sample with TeO2 = 30 mol% (rho = 6.39 g/cm(3)) and 0.1048 cm(-1) for TBBT88 sample with TeO2 = 88 mol% (rho = 5.39 g/cm(3)). Consequently, it can be said that the TBBT30 glass seems to be the most promising shield to be utilized for both gamma and neutron shielding implementations among investigated TBBT glasses.