We present a method for accelerating convergence of Monte Carlo simulations of associating fluids. Such fluids exhibit strong, short-ranged, orientation-specific intermolecular attractions which are difficult to sample via conventional molecular simulation. We propose a bias scheme that preferentially attempts Monte Carlo trials that lead to "unbonding" or "bonding" (UB) transitions of the associating molecules. The proposed method is most like the recently introduced aggregation volume bias Monte Carlo (AVBMC) algorithm of Chen and Siepmann. Both algorithms are much simpler, more efficient, and more generally applicable than previously proposed association-bias schemes. We study the UB algorithm via application to the simple ideal-association model of van Roij. Although unrealistic, the model contains the basic features of association that cause problems for simulation, and its simple nature facilitates analysis of the performance of the simulation algorithm. We find, at least in application to this model, that the UB algorithm exhibits better convergence properties when compared to AVBMC, and through analysis of the acceptance probability distributions we can develop an explanation for this difference. We also demonstrate the UB algorithm in the context of the Gibbs ensemble, reproducing the phase coexistence behavior of a dimerization model originally proposed by Tsangaris and de Pablo.