We search for the standard model Higgs boson produced with a Z boson in 4.1  fb−1 of integrated luminosity collected with the CDF II detector at the Tevatron. In events consistent with the decay of the Higgs boson to a bottom-quark pair and the Z boson to electrons or muons, we set 95% credibility level upper limits on the ZH production cross section multiplied by the H→bb branching ratio. Improved analysis methods enhance signal sensitivity by 20% relative to previous searches. At a Higgs boson mass of 115  GeV/c2 we set a limit of 5.9 times the standard model cross section.