Aerial unmanned vehicles (UAVs) play a significant role in improving the connectivity and coverage of terrestrial communication networks. However, UAV-assisted air-to-ground (A2G) data transmissions usually encounter several fundamental challenges, such as terminal mobility, random nature in channel fading and contention, resource constraints, and application-specific transmission requirements. To tackle these challenges, we formulate a bi-level optimization problem that jointly considers the control of the UAV mobility and transmission power and the scheduling of A2G data transmissions. The objective is to optimize energy consumption and maximize A2G transmission reliability. Particularly, we first theoretically characterize the A2G transmission reliability from a probabilistic perspective concerning the effects of channel fading, channel access contention, and application requirements. We then derive a closed-form expression for the optimal expected transmission reliability. Using the closed-form reliability, we transform the bi-level optimization into a mathematically-tractable optimal control problem and propose an efficient iterative algorithm to solve it. Simulation results show that our approach provides a comprehensive improvement in terms of both energy utilization and A2G transmission reliability, in particular, with a reduction of more than 12.1% in energy consumption and an increase of 7.53% in reliability on average, compared to several baselines.