The motion of a spherical Brownian "probe" particle addressed by an external force immersed in shear flow of a colloidal dispersion of spherical neutrally buoyant "bath" particles is quantified. The steady-state nonequilibrium microstructure of bath particles around the probe-induced by the applied force and ambient shear-is calculated to first order in the volume fraction of bath particles, phi. The distortion to the equilibrium microstructure caused by the moving probe is characterized by a Peclet number Pe(f) (a dimensionless pulling force), and the distortion due to the shear flow is represented by another Peclet number Pe(s) (a dimensionless shear rate). Matched asymptotic expansions are employed to quantify the microstructure at small Peclet numbers; specifically, within the distinguished limits Pe(s)(3/2) << Pe(f) << Pe(s)(1/2) << 1. The nonequilibrium microstructure is subsequently utilized to compute the average rectilinear velocity of the probe through O(phi Pe(s)(3/2)U(s)), for an arbitrary orientation of the external force to the shear flow. Here, U-s is the Stokes velocity of the probe in a pure Newtonian fluid. It is also shown that to O(phi Pe(s)(3/2)U(s)) the torque-free probe simply rotates with the ambient shear; a modification to the angular velocity of the probe is at most O(phi Pe(s)Pe(f)U(s)). In particular, a probe forced along the flow axis of shear is demonstrated to experience a cross-streamline drift velocity of O(phi Pe(s)U(s)) to leading order, which acts to propel the particle to streamlines of the ambient shear that move in the same direction as the external force. A mathematical connection between this result and cross-streamline drift of a particle in a Newtonian fluid at small, but nonzero, Reynolds numbers is drawn. The magnitude of the cross-streamline drift velocity is found to be sensitive to the degree of hydrodynamic interactions between the probe and bath particles, which are tuned via an excluded-annulus model. It is also demonstrated that a probe forced along the vorticity axis of the shear experiences a shear-driven enhancement in rectilinear velocity of O(phi Pe(s)(3/2)U(s)) to leading order: This nonanalytic dependence originates from the microstructural deformation in the shear dominated (outer) region far from the probe. A connection of this finding to recent work on particle sedimentation in orthogonal shear flow of viscoelastic liquids is discussed. (C) 2015 The Society of Rheology.