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Using first-principles calculations, we report on the structural and electronic properties of bilayer hexagonal boron nitride (h-BN), incorporating hydrogen (H-2) molecules inside the cavity for potential H-2-storage applications. Decrease in binding energies and desorption temperatures with an accompanying increase in the weight percentage (upto 4%) by increasing the H-2 molecular concentration hints at the potential applicability of this study. Moreover, we highlight the role of different density functionals in understanding the decreasing energy gaps and effective carrier masses and the underlying phenomenon for molecular adsorption. Furthermore, energy barriers involving H-2 diffusion across minimum-energy sites are also discussed. Our findings provide significant insights into the potential of using bilayer h-BN in hydrogen-based energy-storage applications.