This paper proposed a novel method to determine probabilistic operational safety bound for unmanned aircraft traffic management. The key idea is to implement probabilistic uncertainty quantification and design the operational safety bound shape considering UAV's heading direction. Operational safety bound is used to identify a virtual geographic boundary to protect aircraft and to ensure airspace safety. The proposed operational safety bound is calculated as a function of vehicle performance characteristics, state of vehicle, weather and other probabilistic parameters that affect the real position of vehicle such as position error from the Global Positioning System (GPS). It is calculated individually for each vehicle using real-time data and probability simulation. It considers the heading direction of vehicle and thus it is an anisotropic design. Monte Carlo simulations are conducted to estimate the operational safety bound size with a specified probability of failure. Results indicate that uncertainty is crucial for the operational safety bound's size. Sensitivity study shows that UAV speed has the largest effect on the operational safety bound size. Analysis of impact of failure probability shows that operational safety bound size increases with the decrease in allowable failure probability, but the bound size based on different operational safety bound concept increases at different rate.