  We suggest to study the $B_{s}$ and its excitations $B_{sJ}$ in the $B_c$
decays. We calculate the $B_c\to B_{sJ}$ and $B_c\to B_{J}$ form factors within
the covariant light-front quark model, where the $B_{sJ}$ and $B_{J}$ denote an
s-wave or p-wave $\bar bs$ and $\bar bd$ meson, respectively. The form factors
at $q^2=0$ are directly computed while their $q^2$-distributions are obtained
by the extrapolation. The derived form factors are then used to study
semileptonic $B_c\to (B_{sJ},B_{J})\bar\ell\nu$ decays, and nonleptonic $B_c\to
B_{sJ}\pi$. Branching fractions and polarizations are predicted in the standard
model. We find that the branching fractions are sizable and might be accessible
at the LHC experiment and future high-energy $e^+e^-$ colliders with a high
luminosity at the $Z$-pole. The future experimental measurements are helpful to
study the nonperturbative QCD dynamics in the presence of a heavy spectator and
also of great value for the spectroscopy study.
