Wave-particle interactions between hydromagnetic waves and bounce-resonant ring current ions may cause ions precipitation observed during geomagnetic storms. Uncovering mechanisms of ion loss is important to understanding the recovery phases of these storms. A computer model was developed to numerically solve Hamiltonian guiding center equations of motion for a test particle in a three-dimensional time-dependent electromagnetic field model. The background magnetic field is a simple dipole and hydromagnetic waves are modeled by time-dependent electromagnetic perturbations. Specifically, a single compressional Pc 5 wave well below the ion-cyclotron frequency was used in simulations; the amplitude of the perturbation has been varied up to the maximum observed. Bounce-resonant ring current ions near L = 3 undergo pitch angle scattering and ions are moved along the field line toward the loss cone. Wave perturbations which are superpositions of several different wave modes are also considered. Although bounce-resonant interactions alone cannot account for the observed precipitation, they may be an important part of a multi-step precipitation process.