The high‐bias electrical characteristics of back‐gated field‐effect transistors with chemical vapor deposition synthesized bilayer MoS2 channel and Ti Schottky contacts are discussed. It is found that oxidized Ti contacts on MoS2 form rectifying junctions with ≈0.3 to 0.5 eV Schottky barrier height. To explain the rectifying output characteristics of the transistors, a model is proposed based on two slightly asymmetric back‐to‐back Schottky barriers, where the highest current arises from image force barrier lowering at the electrically forced junction, while the reverse current is due to Schottky‐barrier‐limited injection at the grounded junction. The device achieves a photoresponsivity greater than 2.5 A W−1 under 5 mW cm−2 white‐LED light. By comparing two‐ and four‐probe measurements, it is demonstrated that the hysteresis and persistent photoconductivity exhibited by the transistor are peculiarities of the MoS2 channel rather than effects of the Ti/MoS2 interface.