In this work we present a time-dependent method to evaluate state-to-state reaction probabilities, based on bond coordinates and an adapted body-fixed frame. Such a method is expected to be rather efficient to describe A+BC --> AB+C reactive collisions. In addition, the apparent complexity of the Hamiltonian expressed in these coordinates is reduced when applied to a wave packet represented in grids for the internal coordinates. The efficiency of this method as compared to the use of the most adapted Jacobi coordinates increases as the masses of the satellite atoms approach that of the heavier central atom and, what may be more important, avoids the problems associated with the singularities of the radial kinetic terms in the region of configuration space of interest. This method is used to study the Li+HF(v=0,1,j=0,J=0) reactive collision and the structure of the final state distribution of the LiF products is interpreted in terms of transition state resonances.