Bi-directional communication between humans and swarm systems begs for efficient languages to communicate information between the humans and the Artificial Intelligence (AI)-enabled agents in a manner that is most appropriate for the context. We discuss the criteria for effective teaming and functional bi-directional communication between humans and AI, and the design choices required to create effective languages. We then present a human-AI-teaming communication language inspired by the Australian Aboriginal language of Jingulu, which we call JSwarm. We present the motivation and structure of the language. An example is used to demonstrate how the language operates for a shepherding swarm guidance task.