The structural and electronic properties of hydrogenated bilayer boron nitride (BN) were studied by employing the first-principles calculations. Six major polymorphic structures of hydrogenated bilayer BN are considered. Calculated results show that, among them, the AB-BN and AA-BN structures are the most stable ones. The analysis on the energy bands and electronic properties of the two most stable structures are then performed. Structures of AB-BN and AA-BN are both semiconducting with direct band gaps, and the gaps are 1.47 eV and 1.32 eV, respectively, calculated using the GGA method. Since GGA usually severely underestimates the band gap, the hybrid density functional calculations are then conducted, which suggests that the band gaps are 2.52 eV and 2.34 eV for AB-BN and AA-BN structures, respectively. In the most stable structures of AB-BN and AA-BN, B-N bonds show mainly covalent characters, while B-H and N-H bonds exhibit clear ionic characteristics. Moreover, the band gap of hydrogenated bilayer BN atomic sheet can be continuously modulated by biaxial strains. When the lattice constant is compressed by around 8%, the electronic character of the atomic sheet changes from semiconducting into metallic.