We realized ambipolar field-effect transistors by coupling exfoliated thin flakes of tungsten disulfide (WS2) with an ionic liquid dielectric. The devices show ideal electrical characteristics, including very steep subthreshold slopes for both electrons and holes and extremely low OFF-state currents. Thanks to these ideal characteristics, we determine with high precision the size of the band gap of WS2 ddirectly from the gate-voltage dependence of the source-drain current. Our results demonstrate how a careful use of ionic liquid dielectrics offers a powerful strategy to study quantitatively the electronic properties of nanoscale materials.