  We measure the particle-level forward-backward production asymmetry in
$b\bar{b}$ pairs with masses $m(b\bar{b})$ larger than 150 GeV/$c^2$, using
events with hadronic jets and employing jet charge to distinguish $b$ from
$\bar{b}$. The measurement uses 9.5/fb of ppbar collisions at a center of mass
energy of 1.96 TeV recorded by the CDF II detector. The asymmetry as a function
of $m(b\bar{b})$ is consistent with zero, as well as with the predictions of
the standard model. The measurement disfavors a simple model including an
axigluon with a mass of 200 GeV/$c^2$ whereas a model containing a heavier 345
GeV/$c^2$ axigluon is not excluded.
