  We evaluate theoretically the interaction of the open bottom and strange
systems $\bar B\bar K$, $\bar B^* \bar K$, $\bar B\bar K^*$ and $\bar B^*\bar
K^*$ to look for possible bound states which could correspond to exotic
non--quark-antiquark mesons since they would contain at least one $b$ and one
$s$ quarks. The s-wave scattering matrix is evaluated implementing unitarity by
means of the Bethe-Salpeter equation, with the potential kernels obtained from
contact and vector meson exchange mechanisms. The vertices needed are supplied
from Lagrangians derived from suitable extensions of the hidden gauge symmetry
approach to the bottom sector. We find poles below the respective thresholds
for isospin 0 interaction and evaluate the widths of the different obtained
states by including the main sources of imaginary part, which are the $B^*\to
B\gamma$ decay in the $\bar B^* \bar K$ channels, the $K^*\to K \pi$ in the
channels involving a $K^*$, plus the box diagrams with $\bar B\bar K$ and $\bar
B^*\bar K$ intermediate states for the $\bar B^*\bar K^*$ channels.
