Adaptive shock control bumps can exploit the on-design drag-reducing potential of 2D bumps, while mitigating their off-design performance deterioration through geometric modifications. In this study, experiments and simulations have been employed to investigate the wave-drag reducing potential of (actuated and unconstrained) 2D adaptive shock control bumps over a wide range of shock positions. Experiments were carried out in the Imperial College supersonic wind tunnel, modelling the adaptive bump as a flexible surface placed beneath a Mach 1.4 shock wave. 2D RANS CFD simulations of the flow in a parallel channel with a solid bump complement experiments. Wave drag was demonstrated to be proportional to the ratio of inlet to exit stagnation pressure in a blow-down wind tunnel for a given shock position. The shock exhibits a hysteretic behaviour when travelling in the wind tunnel working section, governed by the wave drag reducing potential of the bump. The actuated adaptive bump tested reduces wave drag over a wider operational envelope than solid bumps as experiments revealed the presence of three preferred structural configurations, which lead to a significantly enlarged hysteresis region. Finally, tests on unconstrained bumps were shown to increase wave drag, both on- and off-design, due to the unfavourable bump shapes that result from (only) passive actuation, suggesting that some constraints are required to achieve desirable surface deformations.