The Higgs boson is the only elementary particle predicted by the Standard Model (SM) that has not yet been observed experimentally. If it exists, it explains the spontaneous electroweak symmetry breaking and the origin of mass for gauge bosons and fermions. We test the validity of the SM by performing a search for the associated production of a Higgs boson and a W boson in the channel where the Higgs boson decays to a bottom-antibottom quark pair and the W boson decays to a charged lepton and a neutrino (the WH channel). We study a dataset of proton-antiproton collisions at a centre-of-mass energy √s = 1.96 TeV provided by the Tevatron accelerator, corresponding to an integrated luminosity of 5.7 fb−1, and recorded using the Collider Detector at Fermilab (CDF).We select events consistent with the signature of exactly one charged lepton (electron or muon), missing transverse energy due to the undetected neutrino (MET) and two collimated streams of particles (jets), at least one of which is required to be identified as originating from a bottom quark. We improve the discrimination of Higgs signal from backgrounds through the use of an artificial neural network. Using a Bayesian statistical inference approach, we set for each hypothetical Higgs boson mass in the range 100-150 GeV/c2 with 5 GeV/c2 increments a 95% credibility level (CL) upper limit on the ratio between the Higgs production cross section times branching fraction and the SM prediction. Our main original contributions are the addition of a novel charged lepton reconstruction algorithm with looser requirements (ISOTRK) with respect the electron or muon tight criteria (TIGHT), as well as the introduction of a novel trigger-combination method that allows to maximize the event yield while avoiding trigger correlations and that is used for the ISOTRK category. The ISOTRK candidate is a high-transverse-momentum good-quality track isolated from other activity in the tracking system and not required to match a calorimeter cluster, as for a tight electron candidate, or an energy deposit in the muon detector, as for a tight muon candidate. The ISOTRK category recovers real charged leptons that otherwise would be lost in the non-instrumented regions of the detector. This allows the reconstruction of more W boson candidates, which in turn increases the number of reconstructed WH signal candidate events, and therefore improves the sensitivity of the WH search. For the TIGHT charged lepton categories, we employ charged-lepton-dedicated triggers to improve the rate of WH signal acceptance during data taking. Since there is no ISOTRK-dedicated trigger at CDF, for the ISOTRK charged lepton category we employ three MET-plus-jets-based triggers. For each trigger we first identify the jet selection where the trigger efficiency is flat with respect to jet information (transverse energy and direction of motion in the transverse plane for the two jets in the event) and then we parametrize the trigger efficiency as a function of trigger MET. On an event-by-event basis, for each trigger we compute a trigger efficiency as a function of trigger parametrization, trigger MET, jet information, trigger prescale and information about whether the trigger is defined or not. For the ISOTRK category we combine the three triggers using a novel method, which allows the combination of any number of triggers in order to maximize the event yield while avoiding trigger correlations. On an event-by-event basis, only the trigger with the largest efficiency is used. By avoiding a logical 'OR' between triggers, the loss in the yield of events accepted by the trigger combination is compensated by a smaller and easier-to-compute corresponding systematic uncertainty. The addition of the ISOTRK charged lepton category to the TIGHT category produces an increase of 33% in the WH signal yield and a decrease of 15.5% to 19.0% in the median expected 95% CL cross-section upper limits across the entire studied Higgs mass interval. The improvement in analysis sensitivity is smaller than the improvement in signal yield because the ISOTRK category has a smaller signal over background ratio than the TIGHT category, due to the looser ISOTRK reconstruction criteria. The observed (median expected) 95% CL SM Higgs upper limits on cross section times branching ratio vary between 2.39 x SM (2.73 x SM) for a Higgs mass of 100 GeV/c2 to 31.1 x SM (31.2 x SM) for a Higgs mass of 150 GeV/c2, while the value for a 115 GeV/c2 Higgs boson is that of 5.08 x SM (3.79 x SM). The novel trigger combination method is already in use by several CDF analyses. It is applicable to any analysis that uses triggers based on MET and jets, such as supersymmetry searches at the ATLAS and CMS experiments at the Large Hadron Collider. In its most general form, the method can be used by any analysis that combines any number of different triggers.