The rate of shrinkage of air bubbles, of initial radius from 50 to 200 microm, injected beneath a planar air-water interface has been measured. Bubbles were stabilized in solutions of 0.05 wt% gelatin or pure beta-lactoglobulin. It has been observed that small size differences between two closely spaced or touching bubbles result in markedly divergent rates of shrinkage for the two. By studying a number of different initial bubble configurations, it is demonstrated that the overall change in bubble size distribution is strongly dependent on local, interbubble gas diffusion. In this respect, the strong tendency for the gelatin-stabilized bubbles to aggregate and shrink, while remaining in contact, produced patterns of disproportionation significantly different from those observed with beta-lactoglobulin. In beta-lactoglobulin solutions, it was usually found that bubbles initially in contact shrank away from each other with time, becoming increasingly isolated as a result. A theoretical approach that can exactly incorporate the perturbation of local diffusion fluxes due to the proximity of two bubbles is presented. This enables one to map a "stability diagram" that delineates regions where the larger bubble of a pair will either shrink or grow, according to the relative size of the bubbles and their separation. Theoretical calculations show that it is possible for a bubble to exhibit more complex shrinkage behavior than is predicted by a mean field approach or the Lifshitz, Slyozov, and Wagner (LSW) theory of Ostwald ripening for dilute systems. The inclusion of dilatational elasticity in the theoretical model introduces additional complications, which are also briefly discussed.