Accurate bacterial identification is vital in medical and healthcare settings. Traditional methods, though reliable, are often time-consuming, underscoring the need for faster, more efficient alternatives. Deep learning-assisted Surface-enhanced Raman spectroscopy (SERS) offers a rapid and sensitive method, demonstrating high accuracy in bacterial identification. However, current deep learning models for bacterial SERS spectra classification typically operate under a closed-set paradigm, limiting their effectiveness when encountering bacterial species outside the training set. In response to this challenge, we propose a transformer-based neural network for open-set bacterial recognition using SERS spectra. Our model utilizes a combination of classification and reconstruction tasks, rejecting unknown species by analyzing reconstruction errors. Experimental results show that the proposed model outperforms traditional open-set recognition approaches, providing superior accuracy in both classifying known species and rejecting unknown ones. This study addresses the limitations of existing closed-set methods, improving the robustness of bacterial identification in real-world scenarios and demonstrating the potential of integrating SERS with transformer models for medical and healthcare applications.