We present the results from a test-particle simulation designed to study how lithium tracer ions injected upstream of the earth's bow shock interact with the bow shock when waves are present in the shock's upstream and downstream vicinity. The wave activity is assumed to consist of parallel and antiparallel propagating Alfv¿n waves characterized by a frequency power spectrum P(f)~f-1 within a frequency interval and range of amplitudes defined separately in the upstream and downstream regions. At a ''single encounter'' (defined in this paper as the time during which an ion remains within ~2 gyroradii of the shock) the waves act mainly to perturb an ion's orbit, leading to an increase (or decrease) in the number of orbital shock crossings, and therefore increase (or decrease) the energy gain (via drift along the U¿B electric field) relative to the situation when waves are absent. Complete transmission of the injected ion distribution is predicted with and without wave activity present when the angle &psgr;1 between the shock normal and the nominal upstream magnetic field satisfies 70¿≲&psgr;1≤90¿. A wave field of sufficient amplitude should increase ion transmission for 45¿≲&psgr;1≲70¿, where significant reflection (~50%) is possible in the absence of waves. At a fixed &psgr;1, increasing wave activity yields larger average energy gains, reduced pitch angle anisotropies, and increased spatial dispersion on the bow shock for both the reflected ions and those transmitted to the magnetosheath.