We present a search for the standard model Higgs boson produced in association with a Z boson in data collected with the CDF II detector at the Tevatron, corresponding to an integrated luminosity of 9.45  fb(-1). In events consistent with the decay of the Higgs boson to a bottom-quark pair and the Z boson to electron or muon pairs, we set 95% credibility level upper limits on the ZH production cross section times the H→bb branching ratio as a function of Higgs boson mass. At a Higgs boson mass of 125  GeV/c(2), we observe (expect) a limit of 7.1 (3.9) times the standard model value.