The elastic properties of the cellular lipid membrane play a crucial role for life. Their alteration can lead to cell malfunction, and in turn, being able to control them holds the promise of effective therapeutic and diagnostic approaches. In this context, due to their proven strong interaction with lipid bilayers, ionic liquids (ILs) - a vast class of organic electrolytes - may play an important role. This work focuses on the effect of the model imidazolium-IL [bmim][Cl] on the bending modulus of DMPC lipid vesicles, a basic model of cellular lipid membranes. Here, by combining small-angle neutron scattering and neutron spin-echo spectroscopy, we show that the IL, dispersed at low concentrations at the bilayer-water interface, (i) diffuses into the lipid region, accounting for five IL-cations for every 11 lipids, and (ii) causes an increase of the lipid bilayer bending modulus, up to 60% compared to the neat lipid bilayer at 40 °C.