Aquatic organisms are known for their ability to generate efficient propulsion with low energy expenditure. While existing research has sought to leverage bio-inspired structures to reduce energy costs in underwater robotics, the crucial role of control policies in enhancing efficiency has often been overlooked. In this study, we optimize the motion of a bio-mimetic robotic fish using deep reinforcement learning (DRL) to maximize propulsion efficiency and minimize energy consumption. Our novel DRL approach incorporates extended pressure perception, a transformer model processing sequences of observations, and a policy transfer scheme. Notably, significantly improved training stability and speed within our approach allow for end-to-end training of the robotic fish. This enables agiler responses to hydrodynamic environments and possesses greater optimization potential compared to pre-defined motion pattern controls. Our experiments are conducted on a serially connected rigid robotic fish in a free stream with a Reynolds number of 6000 using computational fluid dynamics simulations. The DRL-trained policies yield impressive results, demonstrating both high efficiency and propulsion. The policies also showcase the agent's embodiment, skillfully utilizing its body structure and engaging with surrounding fluid dynamics, as revealed through flow analysis. This study provides valuable insights into the bio-mimetic underwater robots optimization through DRL training, capitalizing on their structural advantages, and ultimately contributing to more efficient underwater propulsion systems.