Foundation models like SAM (Segment Anything Model) exhibit strong zero-shot image segmentation performance, but often fall short on domain-specific tasks. Fine-tuning these models typically requires significant manual effort and domain expertise. In this work, we introduce QTT-SEG, a meta-learning-driven approach for automating and accelerating the fine-tuning of SAM for image segmentation. Built on the Quick-Tune hyperparameter optimization framework, QTT-SEG predicts high-performing configurations using meta-learned cost and performance models, efficiently navigating a search space of over 200 million possibilities. We evaluate QTT-SEG on eight binary and five multiclass segmentation datasets under tight time constraints. Our results show that QTT-SEG consistently improves upon SAM's zero-shot performance and surpasses AutoGluon Multimodal, a strong AutoML baseline, on most binary tasks within three minutes. On multiclass datasets, QTT-SEG delivers consistent gains as well. These findings highlight the promise of meta-learning in automating model adaptation for specialized segmentation tasks. Code available at: https://github.com/ds-brx/QTT-SEG/