We present a new search for H0V production, where H0 is a scalar Higgs boson decaying into bb̄ with branching ratio β, and V is a Z0 boson decaying into e+e-, μ+μ-, or νν̄. This search is then combined with previous searches for H0V where V is a W± boson or a hadronically decaying Z0. The data sample consists of 106±4pb-1 of pp̄ collisions at s=1.8TeV accumulated by the Collider Detector at Fermilab. Observing no evidence of a signal, we set 95% Bayesian credibility level upper limits on σ(pp̄→H0V)×β. For H0 masses of 90, 110, and 130GeV/c2, the limits are 7.8, 7.2, and 6.6 pb, respectively.