Delivery drones provide a promising sensing platform for Mobile Crowdsensing (MCS) due to their high mobility and large-scale deployment. However, due to limited battery lifetime and available resources, it is challenging to schedule large-scale delivery drones to derive both high crowdsensing and delivery performance, which is a highly complicated optimization problem with several coupled decision variables. In this paper, we first formalize the delivery drones scheduling problem as a mixed-integer nonlinear programming problem with both sensing and delivery utilities as dual objectives. Then we propose a novel framework DeliverSense with a reinforcement learning-based efficient solution, which decouples the highly complicated optimization search process and replaces the heavy computation via fast approximation. Evaluation results compared with state-of-the-art baseline show that DeliverSense improves the total utility by 13% and 23% on average under various energy budgets and numbers of selected routes, respectively. More importantly, our proposed method achieves much lower computational complexity which is nearly 3 times lower than the baseline.