This work introduces the Sequential Multiple Instance Learning (SMIL) framework, addressing the challenge of interpreting sequential, variable-length sequences of medical images with a single diagnostic label. Diverging from traditional MIL approaches that treat image sequences as unordered sets, SMIL systematically integrates the sequential nature of clinical imaging. We develop a bidirectional Transformer architecture, BiSMIL, that optimizes for both early and final prediction accuracies through a novel training procedure to balance diagnostic accuracy with operational efficiency. We evaluated BiSMIL on three medical image datasets to demonstrate that it simultaneously achieves state-of-the-art final accuracy and superior performance in early prediction accuracy, requiring 30-50% fewer images for a similar level of performance compared to existing models. Additionally, we introduce SMILU, an interpretable uncertainty metric that outperforms traditional metrics in identifying challenging instances.