A full-dimensional time-dependent quantum approach is proposed to study the vibrational predissociation (VP) dynamics of BC-Rg(2) (BC=diatomic molecule, Rg=rare-gas atom) clusters. The method applies the partially-separable time-dependent self-consistent-field approximation to express the six-dimensional total wave function as a product of two wave functions, one describing the three stretching modes of the system, the other one describing the three bending modes. The method is tested by simulating the VP of Cl-2-Ne-2 for the initial Cl-2 vibrational excitations v=7-13, and of I-2(v=21)-Ne-2. The Cl-2-Ne-2 results are compared to experimental data and earlier simulations. The method is very efficient as compared to previous reduced-dimensional quantum models where the bending modes were not explicitly considered in the dynamics. Good agreement with experiment is found for the resonance lifetimes and Cl-2 vibrational distributions for vgreater than or equal to9, where the bending/stretching couplings are not strong. The model underestimates rotational excitation of the Cl-2 fragment, failing to reproduce the Cl-2 rotational distributions. In the case of I-2 (v=21)-Ne-2, the time evolution of the vibrational populations is compared with previous multiconfiguration time-dependent Hartree calculations. The favorable comparison obtained supports the reliability of the method within certain validity conditions.