  We give the first accurate results for $B$ and $B_s$ meson masses from
lattice QCD including the effect of $u$, $d$ and $s$ sea quarks, and we improve
an earlier value for the $B_c$ meson mass. By using the Highly Improved
Staggered Quark action for $u/d$, $s$ and $c$ quarks and NRQCD for the $b$
quarks, we are able to achieve an accuracy in the masses of around 10 MeV. Our
results are: $m_B$ = 5.291(18) GeV, $m_{B_s}$ = 5.363(11) GeV and $m_{B_c}$ =
6.280(10) GeV. Note that all QCD parameters here are tuned from other
calculations, so these are parameter free tests of QCD against experiment. We
also give scalar, $B_{s0}^*$, and axial vector, $B_{s1}$, meson masses. We find
these to be slightly below threshold for decay to $BK$ and $B^*K$ respectively.
