With the advancements in artificial intelligence technology, unmanned aerial vehicles (UAVs) are increasingly being utilized for various smart applications, such as surveillance systems. However, because of their limited computing resources and battery capacity, it is necessary to offload computationally intensive tasks to ground infrastructure, such as edge servers and vehicles. This approach faces challenges, especially in densely populated cities where edge servers may process tasks slower because they receive requests not only from UAVs but also from a number of Internet of Things (IoT) devices. Additionally, in the case of private vehicles, their highly dynamic and unpredictable mobility, coupled with self-interested tendencies may result in a reluctance to share computing resources without incentives. Addressing these limitations, this paper proposes a UAV task offloading scheme utilizing public buses pursuing public service objectives. An optimization problem is formulated to minimize the UAV’s system cost, including energy consumption and task completion delay, and an algorithm based on the successive convex approximation method is introduced. Public bus information and a map of Seoul are utilized in the simulation to ensure the real-world applicability of the proposed method. The simulation results indicate that our method not only reduces the system cost compared with that of other benchmark schemes but also notably improves the task completion rate.