In the prediction of remaining useful life (RUL) for rotating mechanical components, the extraction and construction of health or degradation indicators are crucial. To effectively construct health indicators (HIs) without relying on manual experience, this article proposes an unsupervised method for bearing HI construction and RUL prediction. First, a multiscale convolution and long short-term memory combined autoencoder (MSC-LSTM-AE) network is built to extract encoded features containing time-dependent degradation information. Then, support vector regression (SVR) is employed to calculate anomaly scores based on the encoded features of healthy and faulty data, to construct HIs representing the bearing degradation process. The first prediction time (FPT) is subsequently determined based on the pruned exact linear time (PELT) algorithm to form the crucial series of HI versus RUL. Finally, a prediction network combining a convolutional neural network-bidirectional long short-term memory (CNN-BiLSTM) is utilized and trained for bearing’s RUL prediction. The proposed method is validated on the Xi’an Jiaotong University (XJTU)-Sumyoung Technology Co., Ltd. (SY) bearing dataset, and the experimental results show that the constructed HIs provide a more distinct degradation trend compared to other methods, thereby enhancing RUL prediction performance.