Distance measurements are not the only geometric quantities that can be used for multi-agent formation shape control. Bearing measurements can be used in conjunction with distances. This article employs bearing rigidity for mobile formations, which was developed for robot and sensor network localisation, so that bearings can be used for shape control in mobile formations. The first part of this article examines graph theoretical models for formation network analysis and control law design that are needed to maintain the shape of a formation in two-dimensional space, while the formation moves as a cohesive whole. Bearing-based shape control for a formation of mobile agents involves the design of distributed control laws that ensure the formation moves, so that bearing constraints maintain some desired values. The second part of this article focuses on the design of a distributed control scheme for nonholonomic agents to solve the bearing-based formation shape control problem. In particular, a control law using feedback linearisation is proposed based on shape variables. We simulate the shape control behaviour on differential drive agents for an exemplary bearing rigid formation using the results obtained in the first and second parts of this article.