A measurement of the inclusive bottom jet cross section is presented for events containing a Z boson in pp collisions at 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 ET>20  GeV and |η|<1.5 are identified by reconstructing a secondary decay vertex. The measurement is based on an integrated luminosity of about 330  pb−1. A cross section times branching ratio of σ(Z+b  jets)×B(Z→ℓ+ℓ−)=0.93±0.36  pb is found, where B(Z→ℓ+ℓ−) is the branching ratio of the Z boson or γ∗ into a single flavor dilepton pair (e or μ) in the mass range between 66 and 116  GeV/c2. 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±0.92%. Here, the uncertainties are the quadratic sum of statistical and systematic uncertainties. Predictions made with next-to-leading order QCD agree, within experimental and theoretical uncertainties, with these measurements.