In industrial applications of machinery fault diagnostics, deep learning has been widely adopted to process large amounts of monitoring data. Unfortunately, due to the domain discrepancy, diagnostic models trained with source domain data suffer from degraded diagnostic performance on the target domain. To address this problem, a Wasserstein bi-classifier adversarial learning network (WBALN) is proposed. Specifically, WBALN consists of a feature extractor, two classifiers, and a discrepancy metric based on Wasserstein distance. A two-stream optimization strategy is used in the training process, which involves jointly performing bi-classifier adversarial learning and Wasserstein generative adversarial network (WGAN)-based adversarial learning. In the bi-classifier training stream, a min-max game is conducted between a discrepancy detector composed of two classifiers and the feature extractor to reduce the disparity between these classifiers. In the WGAN-based training stream, a Wasserstein adversarial discrepancy (WAD) is applied in combination with the original classifier as a domain discriminator, which achieves fault diagnosis and distribution alignment through a unified objective. This WAD enables WBALN to achieve sufficient feature alignment using the predicted discriminative information. In addition, the utilization of the nuclear-norm is useful for ensuring the determinacy and diversity of predictions. Except for ordinary domain adaptation, WBALN is also extended for challenging problems about inter-class imbalanced domain adaptation. The performance of the proposed WBALN is verified through multiple experiments on two bearing datasets.