We present measurements of the [Formula: see text] production cross section in b-tagged lepton + jets events from [Formula: see text] collisions at 1.96 TeV using the CDF detector at Fermilab. B-jets are tagged with either a secondary vertex algorithm, or a soft lepton tagger that identifies muons from B hadron semileptonic decays. With Tevatron Run II data, we estimate the [Formula: see text] signal fraction in two different ways: by estimating the various background contributions, and by fitting directly the leading jet transverse energy spectrum for the signal and background contributions. A subset of the sample, with two secondary vertex tagged jets, yields a production cross section consistent with the inclusive measurements. Results are consistent with a Standard Model [Formula: see text] signal and current measurements of the top quark mass.