The bulk viscosity (zeta) of the hadronic medium has been estimated within the ambit of the Hadron Resonance Gas ( HRG) model including the Hagedorn density of states. The HRG thermodynamics within a grand canonical ensemble provides the mean hadron number as well as its fluctuation. The fluctuation in the chemical composition of the hadronic medium in the grand canonical ensemble can result in non- zero divergence of the hadronic fluid flow velocity, allowing us to estimate the zeta of the hadronic matter up to a relaxation time. We study the influence of the hadronic spectrum on zeta and find its correlation with the conformal symmetry breaking measure, is an element of- 3P. We estimate zeta along the contours with constant, S/N-B ( total entropy/net baryon number) in the T - mu plane ( temperature- baryonic chemical potential) for S/N-B = 30, 45 and 300. We also assess the value of zeta on the chemical freeze-out curve for various centers of mass energy ( root s(NN)) and find that the bulk viscosity to entropy density ratio, zeta/s is larger in the energy range of the beam energy scan program of RHIC, low energy SPS run, AGS, NICA and FAIR, than LHC energies.