Batch active learning is a popular approach for efficiently training machine learning models on large, initially unlabelled datasets, which repeatedly acquires labels for a batch of data points. However, many recent batch active learning methods are white-box approaches limited to differentiable parametric models: they score unlabeled points using acquisition functions based on model embeddings or first- and second-order derivatives. In this paper, we propose black-box batch active learning for regression tasks as an extension of white-box approaches: cruicially, our method only relies on model predictions. This approach is compatible with a wide range of machine learning models including regular and Bayesian deep learning models and non-differentiable models such as random forests. This allows us to extend a wide range of existing state-of-the-art white-box batch active learning methods (BADGE, BAIT, LCMD) to black-box models. We evaluate our approach through extensive experimental evaluations on regression datasets, achieving surprisingly strong performance compared to white-box approaches for deep learning models