One-dimensional hybrid simulations of quasi-parallel collisonless shocks have been performed. Alpha particles are included in the simulations self-consistently in such a way that sufficient simulation particles are present to give reasonable statistics. It is found that a fraction of the incoming solar wind protons and alpha particles is accelerated near the shock and escapes upstream. These particles constitute a diffuse upstream particle population. The density ratio bias factor, i.e., the density ratio of diffuse alpha particles to diffuse protons normalized to the solar wind He++ to H+ density ratio varies between 0.5 and 4.0, and depends on the solar wind He++ to H+ density ratio and on the shock Mach number. The density ratio bias factor for a low Mach number shock (MA=4.6) is f~0.5 when the alpha particles are treated as test particles and increases to ~1 when the solar wind ratio of alpha to protons is 0.25. For a high Mach number shock of MA=8.9 with a very small alpha particle contribution to the solar wind we obtained a density ratio bias factor of f~4.