A turbulent separation bubble is forced by single- and double-frequency sinusoidal disturbances, with the emphasis placed on the reattachment length as a function of the forcing amplitude and frequency. The separation bubble is that formed along the side of a blunt circular cylinder with a square leading edge. In single-frequency forcing, the reattachment length attains a minimum at a particular forcing frequency, F, which scales with the frequency of shedding of vortices from the reattachment region of the separated shear layer. A flow model is presented to interpret the frequency F. Forcing of sufficiently high amplitude eliminates the recirculating region in a range of the forcing frequency. Flow visualization and a survey of the mean flow and turbulence properties demonstrate how the flow in the separated shear layer is modified by the forcing. In double-frequency forcing, the superposition of the F-component on its higher or subharmonic components is considered. A non-resonant combination of the two frequencies is also considered.