In multi-cellular organisms, molecular signaling spans multiple distance scales and is essential to tissue structure and functionality. Molecular communications is increasingly researched and developed as a key subsystem in the Internet-of-Nano-Things paradigm. While short range microscopic diffusion communications is well understood, longer range channels can be inefficient and unreliable. Static and mobile relays have been proposed in both conventional wireless systems and molecular communication contexts. In this paper, our main contribution is to analyze the information delivery energy efficiency of bacteria mobile relays. We discover that these mobile relays offer superior energy efficiency compared with pure diffusion information transfer over long diffusion distances. This paper has widespread implications ranging from understanding biological processes to designing new efficient synthetic biology communication systems.