Recent tool-use frameworks powered by vision-language models (VLMs) improve image understanding by grounding model predictions with specialized tools. Broadly, these frameworks leverage VLMs and a pre-specified toolbox to decompose the prediction task into multiple tool calls (often deep learning models) which are composed to make a prediction. The dominant approach to composing tools is using text, via function calls embedded in VLM-generated code or natural language. However, these methods often perform poorly on medical image understanding, where salient information is encoded as spatially-localized features that are difficult to compose or fuse via text alone. To address this, we propose a tool-use framework for medical image understanding called the Tool Bottleneck Framework (TBF), which composes VLM-selected tools using a learned Tool Bottleneck Model (TBM). For a given image and task, TBF leverages an off-the-shelf medical VLM to select tools from a toolbox that each extract clinically-relevant features. Instead of text-based composition, these tools are composed by the TBM, which computes and fuses the tool outputs using a neural network before outputting the final prediction. We propose a simple and effective strategy for TBMs to make predictions with any arbitrary VLM tool selection. Overall, our framework not only improves tool-use in medical imaging contexts, but also yields more interpretable, clinically-grounded predictors. We evaluate TBF on tasks in histopathology and dermatology and find that these advantages enable our framework to perform on par with or better than deep learning-based classifiers, VLMs, and state-of-the-art tool-use frameworks, with particular gains in data-limited regimes. Our code is available at https://github.com/christinaliu2020/tool-bottleneck-framework.