A Bayesian optimisation framework is developed to optimise low-amplitude wall-normal blowing control of a turbulent boundary-layer flow. The Bayesian optimisation framework determines the optimum blowing amplitude and blowing coverage to achieve up to a 5% net-power saving solution within 20 optimisation iterations, requiring 20 Direct Numerical Simulations (DNS). The power input required to generate the low-amplitude wall-normal blowing is measured experimentally for two different types of blowing device, and is used in the simulations to assess control performance. Wall-normal blowing with amplitudes of less than 1% of the free-stream velocity generate a skin-friction drag reduction of up to 76% over the control region, with a drag reduction which persists for up to 650
δ
0
downstream of actuation (where
δ
0
is the boundary-layer thickness at the start of the simulation domain). It is shown that it is the slow spatial recovery of the turbulent boundary-layer flow downstream of control which generates the net-power savings in this study. The downstream recovery of the skin-friction drag force is decomposed using the Fukagata-Iwamoto-Kasagi (FIK) identity, which shows that the generation of the net-power savings is due to changes in contributions to both the convection and streamwise development terms of the turbulent boundary-layer flow.