Due to the uncertainty of the subsurface environment and the complexity of parameters, particularly in feature extraction from input data and when seeking to understand bidirectional temporal information, the evaluation and prediction of the rate of penetration (ROP) in real-time drilling operations has remained a long-standing challenge. To address these issues, this study proposes an improved LSTM neural network model for ROP prediction (CBT-LSTM). This model integrates the capability of a two-dimensional convolutional neural network (2D-CNN) for multi-feature extraction, the advantages of bidirectional long short-term memory networks (BiLSTM) for processing bidirectional temporal information, and the dynamic weight adjustment of the time pattern attention mechanism (TPA) for extracting crucial information in BiLSTM, effectively capturing key features in temporal data. Initially, data are denoised using the Savitzky–Golay filter, and five correlation coefficient methods are employed to select input features, with principal component analysis (PCA) used to reduce model complexity. Subsequently, a sliding window approach transforms the time series into a two-dimensional structure to capture dynamic changes, constructing the model input. Finally, the ROP prediction model is established, and search methods are utilized to identify the optimal hyperparameter combinations. Compared with other neural networks, CBT-LSTM demonstrates superior performance metrics, with MAE, MAPE, RMSE, and R2 values of 0.0295, 0.0357, 9.3101%, and 0.9769, respectively, indicating the highest predictive capability. To validate the model’s robustness, noise was introduced into the training data, and results show stable performance. Furthermore, the model’s predictive results for other wells achieved R2 values of 0.95, confirming its strong generalization ability. This method provides a new solution for ROP prediction in real-time drilling operations, assisting drilling engineers in better planning their operations and reducing drilling cycles.