A single-/dual-band switchable terahertz absorber based on VO₂-BDSs hybrid metamaterial is demonstrated through numerical simulations. When VO₂ is in the insulating state and the Fermi level energy of BDSs is 160 meV, two absorption peaks appear at 0.97 THz and 3.152 THz with absorptivity of 99.3% and 99.7%, respectively. When VO₂ is in the metallic state and the Fermi level energy remains unchanged, the absorber has an absorption peak at 4.246 THz with the value exceeding 98%. By using the phase change characteristics of VO_2,the proposed hybrid metamaterial can switch the absorber from single band to dual band. Due to the existence of BDSs, it is found that the resonance frequency points show a blue shift as the Fermi level energy increases. In order to verify the potential of the proposed metasurface in practical applications, the sensitivity of incident polarization angle is also investigated. Numerical results show that the absorptivity of the proposed absorber remains 90% under large incident angles. The method proposed in this work has potential applications in switching, sensing, and modulation.