  We determine the spectrum of $B_s$ 1P states using lattice QCD. For the
$B_{s1}(5830)$ and $B_{s2}^*(5840)$ mesons, the results are in good agreement
with the experimental values. Two further mesons are expected in the quantum
channels $J^P=0^+$ and $1^+$ near the $BK$ and $B^{*}K$ thresholds. A
combination of quark-antiquark and $B^{(*)}$ meson-Kaon interpolating fields
are used to determine the mass of two QCD bound states below the $B^{(*)}K$
threshold, with the assumption that mixing with $B_s^{(*)}\eta$ and
isospin-violating decays to $B_s^{(*)}\pi$ are negligible. We predict a
$J^P=0^+$ bound state $B_{s0}$ with mass $m_{B_{s0}}=5.711(13)(19)$ GeV. With
further assumptions motivated theoretically by the heavy quark limit, a bound
state with $m_{B_{s1}}= 5.750(17)(19)$ GeV is predicted in the $J^P=1^+$
channel. The results from our first principles calculation are compared to
previous model-based estimates.
