The methods for RUL prediction of bearings are mainly based on the autoregressive strategies, among which the temporal convolutional network (TCN) has been recently developed and widely believed as the high-performance one. These methods generally suffer from the errors of prediction. In this paper, we newly design the Bayesian-optimization-based adversarial temporal convolutional network (AdTCN-BO), by embedding the TCN into the adversarial training framework as the generator. Within the framework, the discriminator is designed to continuously correct the output value of the generator in the training process, thus reducing the errors of prediction to a certain extent. Based on the AdTCN-BO, a novel RUL prediction approach for bearings is developed. An experiment verification is carried out to validate the effectiveness of the proposed approach, demonstrating that the AdTCN-BO framework is more accurate in contrast to the traditional data-driven methods of RUL prediction.