We present a new search for H0V production, where H0 is a scalar Higgs boson decaying into bb with branching ratio beta, and V is a Z0 boson decaying into e+e-, mu+mu-, or nunu. 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 +/- 4 pb(-1) of pp collisions at square root of s = 1.8 TeV accumulated by the Collider Detector at Fermilab. Observing no evidence of a signal, we set 95% Bayesian credibility level upper limits on sigma(pp --> H0V) x beta. For H0 masses of 90, 110, and 130 GeV/c2, the limits are 7.8, 7.2, and 6.6 pb, respectively.