Precision agriculture technologies hold great potential for improving crop monitoring and farming practices. These technologies heavily rely on collecting extensive data through environmental sensors, often scattered over large fields. However, the limited connectivity in rural areas, and the high cost of 4G/5G subscriptions, often hampers their deployment. Unmanned Aerial Vehicles (UAVs) are a valid alternative for sensor data collection across large agricultural fields. However, existing UAV-based solutions often rely on the unnecessary collection of complete information, making them inefficient and more costly. In this paper, we present an innovative framework for collecting agricultural sensor data using UAVs. The framework selects a set of hovering points to visit, from which the data of only a subset of sensors is collected. The data from the remaining sensors is inferred using machine learning. We introduce an optimization problem named Hovering Points Selection (HPS) to select the optimal set of hovering points, and we prove it to be NP-Hard. We then propose a polynomial epsilon(2)-greedy reinforcement learning heuristic, named DRONE (Determining hoveRing pOints with exploratioN and Exploitation), to solve HPS in polynomial time. To further expedite the inference component of DRONE, we also introduce Fast-DRONE, which relies on information theory for hovering point selection. We evaluate the performance of our proposed framework using both synthetic and real agricultural datasets. Results demonstrate up to three times performance improvements over a recent state-of-the-art approach in several scenarios and under different communication technologies.