Dual active bridge converters enable bidirectional power flow in buck and boost operating modes. This paper presents an advanced switching sequence and burst-mode strategy to balance conduction, switching, and magnetic losses under light, medium, and heavy loading conditions, leading to improved operating efficiency. The implementation of the switching sequence employs the natural state-plane trajectories of the converter and contributes to higher efficiency and the ability to perform burst mode. The proposed switching sequences improve the overall efficiency of the converter by enabling soft switching and adjusting the frequency to match the minimum RMS transformer current in the full operating range. Furthermore, it incorporates a fully controlled burst-mode switching sequence for light loading conditions to further extend the efficiency gains. As a result, maximum efficiency is obtained by taking advantage of all the possible switching structures of the converter. The analysis provides insight into the natural trajectories of the converter, which produce soft-switching transitions and enable the converter structures to achieve the target operating point directly. Simulation and experimental results are presented to validate the benefits of the switching sequence and illustrate the burst-mode operation.