A method is presented for determining the bulk velocity on an energetic ion distribution containing a mixture of protons, alpha particles, and heavy ions, measured by a solid state detector system that does not distinguish different ion species. It is applied to the energetic particles anisotropy spectrometer on board ISEE 3 during its deep geotail mission. The measurements at 24 directions and six energy channels (35--619 keV) are fitted to the sum of three ion populations, all subjected to a common velocity transformation. Spectral shapes assumed are a combination of power law and exponential, based on measurements in the deep geomagnetic tail by composition experiments. Very good fits are achieved, and comparison of the result with those of composition experiments are in good agreement. The bulk ion velocities compare favorably to those of the plasma, at least in the plasma sheet. The error in the derived bulk velocity is estimated to be 100 km s-1. Wide differences are seen in the energetic ion boundary layer. Second-order anisotropies are also determined in the moving frame of reference. These can be significantly different from those measured in the spacecraft frame because of the large transformations speeds.