Effective anomaly detection and classification in bridge monitoring data critically depend on robust feature extraction to ensure reliable performance across diverse sensors, loading scenarios, and anomaly types. This study presents a novel deep metric learning-based framework that automates feature extraction, addressing the limitations of traditional manual methods that often lack generalization. The proposed approach employs continuous wavelet transforms to convert time-series signals into time-frequency representations, followed by a convolutional neural network trained with metric learning to produce low-dimensional feature optimized for anomaly classification. These embeddings capture similarities between anomalies, enabling the model to distinguish normal loading events from anomalous ones while classifying specific anomaly types. The method was validated on bridge monitoring data collected from strain gauges and accelerometers under varying loading scenarios, achieving high detection and classification accuracy. This robust and scalable framework highlights the potential of deep metric learning to advance automated bridge monitoring.