Research in developing data-driven models for Air Traffic Management (ATM) has gained a tremendous interest in recent years. However, data-driven models are known to have long training time and require large datasets to achieve good performance. To address the two issues, this paper proposes a Multi-Agent Bidirectional Encoder Representations from Transformers (MA-BERT) model that fully considers the multi-agent characteristic of the ATM system and learns air traffic controllers' decisions, and a pre-training and fine-tuning transfer learning framework. By pre-training the MA-BERT on a large dataset from a major airport and then fine-tuning it to other airports and specific air traffic applications, a large amount of the total training time can be saved. In addition, for newly adopted procedures and constructed airports where no historical data is available, this paper shows that the pre-trained MA-BERT can achieve high performance by updating regularly with little data. The proposed transfer learning framework and MA-BERT are tested with the automatic dependent surveillance-broadcast data recorded in 3 airports in South Korea in 2019.