We study the Murray adaptation of the Noyes--Field five-step model of the BelousovZhabotinsky (BZ) reaction in the case when a tuning parameter r, which determines the level of the bromide ion far ahead of the propagating wave, is bigger than 1 and when the delay in generation of the bromous acid is taken into account. The existence of wavefronts in the delayed BZ system was previously established only in the monostable situation with r \in (0, 1], the physically relevant bistable situation where r > 1 (in real experiments, r varies between 5 and 50) was left open. We complete the study by showing that the BZ system with r > 1 admits monotone traveling fronts. Note that one of the stable equilibria of the BZ model is not isolated. This circumstance does not allow the direct application of the topological or analytical methods previously elaborated for the analysis of the existence of bistable waves.