The attachment of a spherical particle to a bubble is theoretically investigated under the condition of a mixed sorption coating of a collector. It is shown that the attachment is determined primarily by the hydrodynamic factor involving the displacement of liquid from the gap between a bubble and a particle. The dependence of the attachment on the state of the surface of particle (sorption coating) is due to a change in the boundary conditions on the interface with water both in the case of surfactant chemical sorption and in that of the physical adsorption of oil. It is demonstrated that at large distances the thinning of a interlayer is facilitated by a physically sorbed collector, while near the bubble this is done by a chemically sorbed one.