To deal with notorious delays in communication systems, it is crucial to forecast key system characteristics, such as the communication load. Most existing studies aggregate data from multiple edge nodes for improving the forecasting accuracy. However, the bandwidth cost of such data aggregation could be unacceptably high from the perspective of system operators. To achieve both the high forecasting accuracy and bandwidth efficiency, this paper proposes an Adaptive Multi-Teacher Weighting in Teacher-Student Learning approach, namely AdaTeacher, for communication load forecasting of multiple edge nodes. Each edge node trains a local model on its own data. A target node collects multiple models from its neighbor nodes and treats these models as teachers. Then, the target node trains a student model from teachers via Teacher-Student (T-S) learning. Unlike most existing T-S learning approaches that treat teachers evenly, resulting in a limited performance, AdaTeacher introduces a bilevel optimization algorithm to dynamically learn an importance weight for each teacher toward a more effective and accurate T-S learning process. Compared to the state-of-the-art methods, Ada Teacher not only reduces the bandwidth cost by 53.85%, but also improves the load forecasting accuracy by 21.56% and 24.24% on two real-world datasets.