  Excited state spectra of $B$, $B_s$ and $B_c$ mesons are computed using
lattice QCD. Working with a large basis of carefully constructed,
approximately-local $q\bar{q}$-like operators we determine a rich spectrum of
states up to $J=4$ in $B, B_s$ and $B_c$, that can be grouped into patterns
matching those of the quark model. In addition, hybrid-like states are
identified at approximately 1500 MeV above the ground states in each of $B,
B_s$ and $B_c$, in a multiplet pattern already found in similar computations at
a range of quark masses spanning light to bottom. This study is performed using
an anisotropic, relativistic Wilson-clover action at a single spatial lattice
spacing of $a_s\approx 0.12$ fm and with a light-quark mass corresponding to
$m_\pi\approx 391$ MeV. We find good agreement with experimental results where
known and discuss prospects for further work in interesting $J^P$ quantum
numbers.
