An adaptive observer for uniformly observable bilinear systems is proposed in this paper. The adaptive observer is derived from the generalized observer canonical form proposed by Williamson, where the conventional input- and output-injection are replaced by the injection of the output and the derivatives of the input. Then, an output-feedback stabilizing controller, using the observer dependent on the derivatives of the input, is proposed. To avoid the differentiation of the input, integrators are placed at the input channel, which makes the direct design of the controller impossible. To overcome the problem, an indirect design scheme based on backstepping is proposed.