Affective sharing within groups strengthens coordination and empathy, leads to better health outcomes, and increases productivity and performance. Existing tools for affective sharing face one main challenge: creating a representation of collective emotional states that is relatable and universally accessible. To overcome this challenge, we propose HeartBees, a bio-feedback system for visualizing collective emotional states, which maps a multi-dimensional emotion model into a metaphorical visualization of flocks of birds. Grounded on Affective Computing literature and physiological sensing, we mapped physiological indicators that could be obtained from wearable devices into a multi-dimensional emotion model, which, in turn, our HeartBees can make use of. We evaluated our nature-inspired interactive system with 353 online participants, whose responses showed good consensus in the way they subjectively perceived the visualizations. Last, we discuss practical applications of HeartBees.