Acoustic scene classification (ASC) predominantly relies on supervised approaches. However, acquiring labeled data for training ASC models is often costly and time-consuming. Recently, self-supervised learning (SSL) has emerged as a powerful method for extracting features from unlabeled audio data, benefiting many downstream audio tasks. This paper proposes a data-efficient and low-complexity ASC system by leveraging self-supervised audio representations extracted from general-purpose audio datasets. We introduce BEATs, an audio SSL pre-trained model, to extract the general representations from AudioSet. Through extensive experiments, it has been demonstrated that the self-supervised audio representations can help to achieve high ASC accuracy with limited labeled fine-tuning data. Furthermore, we find that ensembling the SSL models fine-tuned with different strategies contributes to a further performance improvement. To meet low-complexity requirements, we use knowledge distillation to transfer the self-supervised knowledge from large teacher models to an efficient student model. The experimental results suggest that the self-supervised teachers effectively improve the classification accuracy of the student model. Our best-performing system obtains an average accuracy of 56.7%.