  At hadron colliders the dominant production mechanism of $(\bar bc)$ mesons
with large transverse momentum is due to parton fragmentation. We compute the
rates and transverse momentum spectra for production of S-wave and P-wave
$(\bar b c)$ mesons at the Tevatron via the direct fragmentation of the bottom
antiquark as well as the Altarelli-Parisi induced gluon fragmentation. Since
all the radially and orbitally excited $(\bar b c)$ mesons below the $BD$
flavor threshold will cascade into the pseudoscalar ground state $B_c$ through
electromagnetic and/or hadronic transitions, they all contribute to the
inclusive production of $B_c$. The contributions of the excited S-wave and
P-wave states to the inclusive production of $B_c$ are 58 and 23\%,
respectively, and hence significant.
