Bayesian Active Learning has had significant impact to various NLP problems, but nevertheless it's application to text summarization has been explored very little. We introduce Bayesian Active Summarization (BAS), as a method of combining active learning methods with state-of-the-art summarization models. Our findings suggest that BAS achieves better and more robust performance, compared to random selection, particularly for small and very small data annotation budgets. Using BAS we showcase it is possible to leverage large summarization models to effectively solve real-world problems with very limited annotated data.