  A measurement of the inclusive bottom jet cross section is presented for
events containing a $Z$ boson in $p\bar{p}$ collisions at $\sqrt{s}=1.96$ TeV
using the Collider Detector at Fermilab. $Z$ bosons are identified in their
electron and muon decay modes, and $b$ jets with $E_T>20$ GeV and $|\eta|<1.5$
are identified by reconstructing a secondary decay vertex. The measurement is
based on an integrated luminosity of about 330 ${\rm pb}^{-1}$. A cross section
times branching ratio of $\sigma (Z+b {\rm jets}) \times {\cal B}(Z \to \ell^+
\ell^-)= 0.93 \pm 0.36$ pb is found, where ${\cal B}(Z\to \ell^+ \ell^-)$ is
the branching ratio of the $Z$ boson or $\gamma^*$ into a single flavor
dilepton pair ($e$ or $\mu$) in the mass range between 66 and 116 GeV$/c^2$.
The ratio of $b$ jets to the total number of jets of any flavor in the $Z$
sample, within the same kinematic range as the $b$ jets, is $2.36 \pm 0.92%$.
Here, the uncertainties are the quadratic sum of statistical and systematic
uncertainties. Predictions made with NLO QCD agree, within experimental and
theoretical uncertainties, with these measurements.
