This paper proposes a novel distributed active sensing control strategy for formations of drones measuring relative bearings. To be able to localize their relative positions from bearing measurements, the drone formation must satisfy specific Persistency of Excitation (PE) conditions. We propose a solution that can meet these PE conditions by maximizing the information collected from onboard cameras via a distributed gradient-based algorithm. Additionally, we also consider presence of a (concurrent) position-based formation control task using Quadratic Program-based control with Control Lyapunov Functions (CLFs). The results show that the inclusion of active sensing in the formation control law significantly enhances the localization accuracy and, as a consequence, the precision of reaching the desired formation. The improvement is especially important when the underlying graphs are not Infinitesimally Bearing Rigid (IBR), as it can be expected.