  We report a measurement of the production cross section for b hadrons in
p-pbar collisions at sqrt{s}=1.96 TeV. Using a data sample derived from an
integrated luminosity of 83 pb^-1 collected with the upgraded Collider Detector
(CDF II) at the Fermilab Tevatron, we analyze b hadrons, H_b, partially
reconstructed in the semileptonic decay mode H_b -> mu^- D^0 X. Our measurement
of the inclusive production cross section for b hadrons with transverse
momentum p_T > 9 GeV/c and rapidity |y|<0.6 is sigma = 1.30 mub +/- 0.05
mub(stat) +/- 0.14 mub (syst) +/- 0.07 mub (B), where the uncertainties are
statistical, systematic, and from branching fractions respectively. The
differential cross sections dsigma/dp_T are found to be in good agreement with
recent measurements of the H_b cross section and well described by fixed-order
next-to-leading logarithm predictions.
