This supplementary material includes further details on the typical tuning characteristics of bubble-free resonators (S.I), frequency scanning slices at various gate voltages (S.II), finite element simulation of bubble effects on resonant characteristics (S.III), feasibility analysis of "Bubble growth" (S.IV), relaxation of the fluctuations in resonant frequency and quality factor (S.V), another mode that is discernible at low gate voltages (S.VI), hysteresis effects during bidirectional gate voltage sweeps (S.VII), AFM and SEM characterization of interfacial bubbles in heterostructures (S.VIII), another identically processed bubble-free h-BN/Gra heterostructure and its tuning characteristics (S.IX), another h-BN/Gra heterostructure resonator with interfacial bubbles and its tuning characteristics (S.X), as well as the impact of bubble quantity and distribution on resonant dispersion characteristics (S.XI).