This study aims to classify sleep stages using electroencephalogram (EEG) signals to investigate the potential impact of entrepreneurial stress on the sleep quality of entrepreneurial students. Due to high stress and irregular schedules, entrepreneurial students are prone to sleep issues, making accurate detection and analysis of their sleep states highly significant in practice. This study proposes a lightweight deep learning model that combines Depthwise Separable Convolution (DSC) with a Bidirectional Long Short-Term Memory (Bi-LSTM) network to capture the spatiotemporal features of EEG signals. DSC effectively extracts spatial features from EEG data, reducing model complexity and computational cost, while Bi-LSTM enhances the model’s ability to capture temporal dependencies, thereby improving the identification of different sleep stages (W, N1, N2, N3, and REM). This approach balances efficiency and accuracy, making it suitable for environments with limited computational resources. Experiments were conducted on both the public Sleep-EDF dataset and a custom dataset collected from entrepreneurial students. The results show that the model achieved a sleep stage classification accuracy of 93.59% on the Sleep-EDF dataset and 88.98% on the custom entrepreneurial student dataset, demonstrating strong generalization and robustness. Additionally, the model maintained high F1-scores across different sleep stages, with particularly outstanding performance in the classification of N2 and REM stages. This study provides an efficient and interpretable tool for monitoring the sleep health of entrepreneurial students, contributing to further understanding of the relationship between sleep and entrepreneurial psychological states. It offers scientific support for enhancing the health management and learning efficiency of entrepreneurial students.