A numerical simulation is used to determine the dissolution rate of a freely rising bubble in both pure water and aqueous surfactant solutions. Results are presented for three different gases representing a broad range of solubilities. In pure water, highly soluble gases dissolve more slowly than one would expect from a quasi-steady boundary layer theory. It is argued that this is a consequence of the effect of the moving boundary. While surfactants strongly affect the dissolution rate for gases with small solubilities, they have relatively little effect on gases with large solubilities. The effects of surfactant sorption kinetics are investigated using the Langmuir model. Over a broad range of sorption parameters, a surfactant cap forms and grows as the bubble accelerates. For highly soluble gases, the surfactant cap is too small to significantly affect the dissolution process until most of the bubble's mass is gone. A criterion for a critical surfactant concentration below which the surfactant has relatively little effect on the bubble is developed and tested with the simulations. For a range of surfactant concentrations, a bubble can achieve a maximum speed that is larger than the steady-state speed of a non-dissolving bubble. A criterion for the critical surfactant concentration below which this will occur is developed and tested with the simulations.