The classification of nonstationary data streams presents a substantial challenge mainly due to the simultaneous presence of class imbalance and concept drift. Ensemble learning is a widely acknowledged approach to address these two problems. Nevertheless, most of the existing methods establish independent strategies for each, ignoring their relationship and interactions, which prevents the corresponding strategies from performing as expected. This paper presents a novel algorithm AB-DES (Adaptive Bagging-based Dynamic Ensemble Selection), which employs bagging technique and dynamic ensemble selection system. In AB-DES, instances are stored to balance subsequent data chunks instead of relying solely on resampling methods. Then, all base classifiers are updated using a new dual adaptive sampling bagging strategy, which can help to reduce the classification inaccuracies involving by class imbalance. In the prediction phase, DES system constructs different ensemble models for different instances. The inclusion of a sliding window-based drift detector makes the above two strategies adapt to concept drift. Experimental results show that AB-DES achieves higher classification accuracy and exhibits enhanced robustness compared to 8 state-of-the-art methods on 10 synthetic datasets and 5 real world datasets with different types of concept drift.