Trophallaxis is the mutual exchange and direct transfer of liquid food among eusocial insects such as ants, termites, wasps, and bees. This process allows efficient dissemination of nutrients and is crucial for the colony's survival. In this paper, we present a data-driven agent-based model and use it to explore how the interactions of individual bees, following simple, local rules, affect the global food distribution. We design the rules in our model using laboratory experiments on honeybees. We validate its results via comparisons with the movement patterns in real bees. Using this model, we demonstrate that the efficiency of food distribution is affected by the density of the individuals, as well as the rules that govern their behavior: e.g., how they move and whether or not they aggregate. Specifically, food is distributed more efficiently when donor bees do not always feed their immediate neighbors, but instead prioritize longer motions, sharing their food with more-distant bees. This non-local pattern of food exchange enhances the overall probability that all of the bees, regardless of their position in the colony, will be fed efficiently. We also find that short-range attraction improves the efficiency of the food distribution in the simulations. Importantly, this model makes testable predictions about the effects of different bee densities, which can be validated in experiments. These findings can potentially contribute to the design of local rules for resource sharing in swarm robotic systems.