The bismuth-based non-toxic and lead-free alloys have been investigated for their advanced photon attenuation and photon energy absorption characteristics over wide $\gamma$-ray energy regime from 1 keV to 20 MeV. For this study, we selected five bismuth containing alloys with composition: Bi50Sn(50 − $x$)Zn$x$ where $x =$ 0, 10, 20, 30, 40 wt.%. The mass attenuation coefficient values computed by theoretical approach using the WinXCom software package show marked difference from the mass energy-absorption coefficient values particularly in the energy regime dominated by the Compton effect (CE). Photon interaction (attenuation) effective atomic number ($Z_{{\rm PIeff}}$) and photon-energy absorption effective atomic number ($Z_{{\rm PEAeff}}$) values were compared for their mean, maximum and minimum values computed for these alloys. The optimum thickness range analysed using the attenuation and absorption coefficient values indicate saturation with respect to photon energy spanning Compton effect (CE) and pair-production (PP) processes. Kinetic energy released per unit mass of the absorbing material (KERMA) relative to air calculations indicated significant influence of the elemental composition of these alloys in the intermediate photon energy regime. We also performed calculations for the air-KERMA or exposure build-up factors of these Bi–Sn–Zn alloy compositions done within the framework of novel EXABCal programme code. The calculated exposure build-up factor was found to be minimum for the alloy composition Bi50Sn50. Present investigation of photon interaction and photon energy absorption characteristics would be of interest for addressing shielding efficiency of lead-free and environment friendly bismuth containing alloy systems.