Irregular Medical Time Series play a critical role in the clinical domain to better understand the patient's condition. However, inherent irregularity arising from heterogeneous sampling rates, asynchronous observations, and variable gaps poses key challenges for reliable modeling. Existing methods often distort temporal sampling irregularity and missingness patterns while failing to capture variable decay irregularity, resulting in suboptimal representations. To address these limitations, we introduce DBGL, Decay-Aware Bipartite Graph Learning for Irregular Medical Time Series. DBGL first introduces a patient-variable bipartite graph that simultaneously captures irregular sampling patterns without artificial alignment and adaptively models variable relationships for temporal sampling irregularity modeling, enhancing representation learning. To model variable decay irregularity, DBGL designs a novel node-specific temporal decay encoding mechanism that captures each variable's decay rates based on sampling interval, yielding a more accurate and faithful representation of irregular temporal dynamics. We evaluate the performance of DBGL on four publicly available datasets, and the results show that DBGL outperforms all baselines.