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We interpret the $B_{s1}(5778)$ as an $S$-wave $B^\ast\bar{K}$ molecularstate in the Bethe-Salpeter equation approach. In the ladder and instantaneousapproximations, and with the kernel containing one-particle-exchange diagramsand introducing three different form factors (monopole, dipole, and exponentialform factors) in the vertex, we find the bound state exists. We also study thedecay widths of the decay $B_{s1}(5778)\rightarrow B_s^\ast\pi$ and theradiative decays $B_{s1}(5778)\rightarrow B_s\gamma$ and$B_{s1}(5778)\rightarrow B_s^{\ast}\gamma$, which will be instructive for theforthcoming experiments.

$B_{s1}(5778)$ as a $B^*\bar{K}$ molecule in the Bethe-Salpeter equation approach