Today's software is bloated leading to significant resource wastage. This bloat is prevalent across the entire software stack, from the operating system, all the way to software backends, frontends, and web-pages. In this paper, we study how prevalent bloat is in machine learning containers. We develop MMLB, a framework to analyze bloat in machine learning containers, measuring the amount of bloat that exists on the container and package levels. Our tool quantifies the sources of bloat and removes them. We integrate our tool with vulnerability analysis tools to measure how bloat affects container vulnerabilities. We experimentally study 15 machine learning containers from the official Tensorflow, Pytorch, and NVIDIA container registries under different tasks, (i.e., training, tuning, and serving). Our findings show that machine learning containers contain bloat encompassing up to 80\% of the container size. We find that debloating machine learning containers speeds provisioning times by up to $3.7\times$ and removes up to 98\% of all vulnerabilities detected by vulnerability analysis tools such as Grype. Finally, we relate our results to the larger discussion about technical debt in machine learning systems.