In this paper we calculate the shear-induced self and gradient diffusivities in a dilute bidisperse suspension of hard spheres. Unlike the interaction of identical spheres, the center of mass of a pair of unequally sized spheres does not translate with the imposed shear flow and hence the radial and tangential drifts of the center of mass were tracked using appropriately defined mobility functions. Results of the trajectory calculations show that the minimum surface-to-surface distance xi (min) of the limiting closed orbit trajectories was a minimum for equally sized spheres (size ratio lambda = 1) and monotonically increased for lambda --> 0 and lambda --> infinity. In addition to purely hydrodynamic interactions, trajectories and diffusivities are examined for the case where the hard-sphere radius exceeds the true radius by a factor of (1 + epsilon (s)) such as what would be found for rough spheres (da Cunha, F: R., and Hinch, E. J., J. Fluid Mech. 309, 211 (1996)). The force of one sphere on the other at contact was shown to be a strong function of the size ratio lambda, with the force being maximum for the equally sized sphere case. The tracer diffusivities were analytically solved for the case where hydrodynamics were absent. For this case, the diffusivities were seen to increase with lambda for a dimensionless separation distance, epsilon (s) << 1, as a result of the increased rate of interaction between a large test sphere and the small background spheres. On the other hand, for epsilon (s) >> 1 and lambda the diffusivities were seen to be decreasing functions of lambda. A comparison with numerical results shows that the two match in the far-field limit, while they diverge when hydrodynamic interactions become important in the near-field limit. Finally, gradient diffusivities D-C were calculated analytically and numerically and were found to be roughly an order of magnitude greater than the corresponding tracer diffusivities.