Formation control of multi-agent systems deals with groups of robots forming specific spatial geometries. Combined with the advancements of unmanned aerial vehicles (UAVs) in the past decade, formation control may potentially be applied to tasks such as search-and-rescue, surveillance, even collaborative manipulation. A key challenge is the decentralization of formation control, where each agent behaves independently using onboard sensors and computation, improving the scaleability and robustness of the system. This paper proposes a decentralized controller based on model predictive control (MPC), for the control of formations of quadrotor UAVs defined by inter-agent bearings. The use of MPC allows the controller to account for attitude kinematics, improving upon the results of existing bearing formation control methods based on rigidity and visual servoing approaches, which typically only consider the quadrotor as a single or double integrator. Furthermore the near-optimality of MPC permits a more optimal use of the quadrotors dynamic capabilities for faster maneuvering. Extensive simulations are performed to demonstrate the improved transient formation convergence and fast maneuvering permitted by this controller. Experiments show that it is indeed a real-time feasible solution for bearing formation control.