This paper introduces a simple and very efficient strategy to extrinsically calibrate a bearing sensor (e.g. a camera) mounted on a mobile robot and simultaneously estimate the parameters describing the systematic error of the robot odometry system. The paper provides two contributions. The first one is the analytical computation to derive the part of the system which is observable when the robot accomplishes circular trejectories. This computation consists in performing a local decomposition of the system, based on the theory of distributions. In this respect, this paper represents the first application of the distribution theory in the frame-work of mobile robotics. Then, starting from this decomposition, a method to efficiently estimate the parameters describing both the extrinsic bearing sensor calibration and the odometry calibration is derived (second contribution). Simulations and experiments with the robot e-Puck equipped with encoder sensors and a camera validate the approach.