Maintaining a stable formation among nonholonomic unicycles presents a significant challenge, particularly when subjected to real-world disturbances such as wheel slipping and motor noise. To tackle this issue, we propose a conditional disturbance utilization (CDU) framework that selectively uses favorable disturbances rather than simply rejecting all. First, the disturbance observer (DO) is employed to establish the informational foundation for subsequent conditional utilization decisions. And, the CDU mechanism dynamically decides whether the disturbance aligns with the desired control objective. Moreover, incorporating bearing rigidity achieves global stability with fast convergence. Specifically, the proposed potential function, constructed from bearing information, mitigates disturbance driven collision risks and ensures safety. Finally, simulations and experiments validate the proposed CDU-based formation control. The results demonstrate substantial improvements in responsiveness, and efficiency when compared to disturbance suppression method, highlighting the superiority of the proposed framework.