This study presents an initial study on the adaptive bistable stiffness of the hair cell bundle structure in a frog cochlea, and aims to harness its bistable nonlinearity that features a negative stiffness region for broadband vibration applications such as vibration-based energy harvesters. To this end, the mathematical model for describing the bistable stiffness is first formulated based on the modeling concept of piecewise type nonlinearities. The harmonic balance method was then employed to examine the nonlinear responses of bistable oscillator, mimicking hair cells bundle structure under the frequency sweeping condition, and their dynamic behaviors induced by bistable stiffness characteristics are projected on phase diagrams, and Poincare maps concerning the bifurcation. In particular, the bifurcation mapping at the super- and sub-harmonic regimes provides a better perspective to examine the nonlinear motions which occur in the biomimetic system. The use of bistable stiffness characteristics of hair cell bundle structure in frog cochlea thus offers physical insights to harness the adaptive bistable stiffness for metamaterial-like potential engineering structures such as vibration-based energy harvester, and isolator etc.