Millimeter-sized bubbles rise through most liquids with Reynolds numbers of several hundred. A boundary layer solution is given for flow over the upper surface of spherical or spherical-cap bubbles when surface-active solutes adsorb on the bubble interface and inhibit its motion. Diffusion of adsorbed surfactant along the interface is shown to be negligible. The surfactant accumulates not as a cap around the bottom of the bubble, as in the creeping-flow case, but in a band around the flow separation point from where it desorbs back into solution. The bubble interface is stationary at, or slightly above (if diffusion along the interface is considered), the flow separation point. As much surfactant desorbs from as adsorbs to the interface in the boundary-layer region, and since this equality must hold for the whole bubble, it is also true for the wake region. The flow separation angle moves from 130-degrees to 80-degrees with increasing surfactant concentration. This may, however, also reflect a change in bubble shape since the accumulation of surfactant reduces the interfacial tension and could be producing the sharp corner characteristic of the flow separation point in spherical-cap bubbles.