In this work, we study possible hidden-bottom molecular pentaquarks $P_b$ from coupled-channel $Sigma^{(*)}_bB^{(*)}-Lambda_bB^{(*)}$ interaction in the quasipotential Bethe-Salpeter equation approach. In isodoublet sector with $I=1/2$, with the same reasonable parameters the interaction produces seven molecular states, a state near $ Sigma_bB$ threshold with spin parity $J^P=1/2^-$, a state near $Sigma^*_bB$ threshold with $3/2^-$, two states near $Sigma_bB^*$ threshold with $1/2^-$ and $3/2^-$, and three states near $Sigma_b^*B^*$ threshold with $1/2^-$, $3/2^-$, and $5/2^-$. The results suggest that three states near $Sigma_b^* B^*$ threshold and two states near $Sigma_b B^*$ threshold are very close, respectively, which may be difficult to distinguish in experiment without partial wave analysis. Compared with the hidden-charm pentaquark, the $P_b$ states are relatively narrow with widths at an order of magnitude of 1 MeV or smaller. The importance of each channel considered is also discussed, and it is found that the $Lambda_b B^*$ channel provides important contribution for the widths of those states. In isoquartet sector with $I=3/2$, cutoff should be considerably enlarged to achieve bound states from the interaction, which makes the existence of such states unreliable. The results in the current work are helpful for searching for hidden-bottom molecular pentaquarks in future experiments, such as the COMPASS, J-PARC, and the Electron Ion Collider in China (EicC).
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