The dissipation of the flow kinetic energy of solar wind ions at the quasi-perpendicular bow shock results in the formation of ion distributions that have large perpendicular temperature anisotropies. These anisotropies provide free energy for the growth of Alfv¿n ion cyclotron (A/IC) and mirror waves. The waves then make the ion distributions gyrotropic and substantially reduce their anisotropy. Although differences exist, many of the mechanisms governing wave generation and particle isotropization operate at both high and low Mach number shocks. These mechanisms are easier to study at low Mach number shocks because they proceed relatively slowly and the turbulence level is lower. Also, in general, the plasma beta is lower at the low Mach number bow shock, allowing for situations in which minority ion species like He++ can suppress proton cyclotron waves and thus play a larger role in sheath dynamics than they do at high Mach number shocks. For these reasons, we use two-dimensional hybrid simulations to model the heating of H+ and He++ ions at the low Mach number bow shock and examine wave excitation and ion isotropization in the magnetosheath downstream. In agreement with observations and theory and in contrast to high Mach numbers, we find that the magnetosheath turbulence mostly consists of A/IC waves. Without helium ions, the A/IC wave activity is dominated by parallel propagating proton cyclotron waves. When helium ions are included at a low density, they tend to absorb these waves, leaving obliquely-propagating A/IC waves dominant, though at a lower intensity level. Proton heating at the shock is dominated by bulk perpendicular heating of the core, while the helium ions are heated only slightly. Instead, initially they gyrate around field lines downstream as a coherent, nongyrotropic bunch. Downstream, the protons are slowly isotropized through pitch-angle scattering by A/IC waves. The helium ions undergo perpendicular heating through absorption of proton waves and become more gyrotropic. The perpendicular heating drives the growth of helium cyclotron waves, which in turn reduce the anisotropy of the helium ions. Far downstream of the shock, obliquely-propagating helium cyclotron waves dominate the sheath turbulence.¿ 1996 American Geophysical Union