Using data collected during the 1992-1993 collider run at Fermilab,
CDF has reconstructed several hundred charmed mesons
($D^0$, $D^+$, $D^{*+}$ and $D_s$) in association with leptons from $B$
semileptonic decays. We report on a measurement of the cross section of
$B$ and $B_s$ mesons as a function of transverse momentum using this sample.
The observation of a charmed meson eliminates many systematic uncertainties
in the background subtraction inherent in previous measurements from
inclusive lepton samples, and allows the backgrounds to be measured
from the data. The $B$ meson $p_T$ range probed by the lepton+charm
technique is 18 GeV and above, and thus these measurements complement
similar measurements at lower $p_T$ in the fully exclusive channels
$B \rightarrow J/\psi K$ and $B \rightarrow J/\psi K^*$. Results are
compared to other Tevatron measurements and Next-To-Leading-Order QCD
predictions.