A measurement of the inclusive bottom jet cross section is presented for events containing a $Z$ boson in $pbar{p}$ 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 ${cal B}(Zto ell^+ ell^-)$ 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.
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