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Employing a mobile sink (MS) to act as a relay node in wireless sensor network (WSN) applications is a promising solution for efficient power saving and data collection. However, establishing long-distance traveling leads to larger latency or inefficient buffer management at rendezvous points (RPs), e.g., flying UAVs in disaster management. Moreover, there is no efficient solution to guarantee the completeness of data gathering by considering the waiting time (sojourn) of the MS to receive packets from RPs in addition to the MS moving time among RPs. This work presents a rate-adaptation and buffer-awareness data gathering for MS scheduling (RBDMS) by constructing grid cells in the monitoring area. In fact, it establishes the shortest path by passing within the communication range of the sensors based on data volume. RBDMS not only has a mechanism for handling emergency packets with low latency but also benefits from stochastic integer programming (SIP) for scheduling the MS sojourn time with lower computational time using Lagrangian relaxation. Simulation results confirm that the proposed RBDMS outperforms comparable state-of-the-art works in terms of the MS path length, network lifetime, the energy consumption of sensors, and MS, as well as buffering performance.