Brownian and molecular dynamics simulations are used to study rapid bimolecular reactions at near-infinite dilution in near-critical and supercritical fluids. We probe the dynamics of both nonreactive and reactive collisions and measure rate constants for reaction and collision. Collision rate constants are nearly independent of bulk solvent density, but affected by local solute-solute density enhancements at a given density : their magnitudes depend on the length scale for molecular encounters (cybotactic radius) in the reaction through the equilibrium solute-solute radial distribution function. In contrast, reaction rate constants asymptotically approach the gas-kinetic limit at low densities and the Smoluchowski liquid-like limit at high densities. They also display the same radial dependence as collision rate constants at lower densities and a direct dependence on the cybotactic radius at higher densities (as in the Smoluchowski theory). Their behavior is explained in terms of a transition from a collision-limited regime at low densities to a diffusion-limited regime at higher densities. The transition between these regimes depends on the cybotactic radius and the density of the system, the interplay of which causes shifts in the transition region which depend not only on the properties of the near-critical solvent : they differ for different reactions, even at the same solvent density. This explains some of the apparent inconsistencies among previous experimental and computational studies of reactions in supercritical fluid media.