When bubbles rise through a liquid they are known to scavenge dissolved surface-active materials (surfactants). Small bubbles in the size range of tens of micrometers quickly become covered with surfactants in any but the cleanest conditions. This has the effect of immobilizing the bubble surface and affecting the drag and therefore the bubble rise speed. A large number of bubbles rising as a cloud toward a free surface will populate the bulk surface with surfactants at a richness that far exceeds that which would occur in the absence of bubbling. However, in addition to the increased deposition of surfactants on the bulk surface, the random and agitated motions of the rising bubbles induce mixing of the liquid. In a companion paper (R. L. Stefan and A. J. Szeri, submitted for publication) the mixing properties of a bubble cloud rising toward a free surface were determined. In the present work, a model for the uptake of surfactants by bubbles and subsequent deposition on the bulk surface is developed including the crucial feature of bubble-induced fluid mixing. It is found that the mixing of desorbed surfactant down into the bulk is key to predicting what will be the enrichment of the bulk surface.