We present a search for Higgs bosons decaying into bb and produced in association with W bosons in pp collisions at s√=1.96  TeV. This search uses 320  pb−1 of the data set accumulated by the upgraded Collider Detector at Fermilab. Events are selected that have a high-transverse momentum electron or muon, missing transverse energy, and two jets, at least one of which is consistent with the hadronization of a b quark. Both the number of events and the dijet mass distribution are consistent with standard model background expectations, and we set 95% confidence level upper limits on the production cross section times branching ratio for the Higgs boson or any new particle with similar decay kinematics. These upper limits range from 10 pb for mH=110  GeV/c2 to 3 pb for mH=150  GeV/c2.