The unique property of bilayer graphene to show a band gap tunable by external electrical fields enables a variety of different device concepts with novel functionalities for electronic, optoelectronic, and sensor applications. So far the operation of bilayer graphene-based field effect transistors requires two individual gates to vary the channel's conductance and to create a band gap. In this paper, we report on a method to increase the on/off ratio in single gated bilayer graphene field effect transistors by adsorbate doping. The adsorbate dopants on the upper side of the graphene establish a displacement field perpendicular to the graphene surface breaking the inversion symmetry of the two graphene layers. Low-temperature measurements indicate that the increased on/off ratio is caused by the opening of a mobility gap.