Detecting front-end JavaScript libraries in web applications is essential for website profiling, vulnerability detection, and dependency management. However, bundlers like Webpack transpile code in various ways, altering the original directory and code structure, which complicates library detection. While state-of-the-art techniques utilize property pattern-based library detection at runtime, they face two key limitations: (1) they cannot detect libraries inaccessible from the global object, and (2) they have limitations in granular version detection. To address these challenges, we present DEBUN, a scalable technique for detecting JavaScript libraries and their versions using function-level fingerprints. Our key insight is that bundlers preserve the property names and execution order of property operations, even after transpilation. To leverage this, we introduce the property-order graph (POG), which represents the execution order of property operations within a function body. We evaluate DEBUN on 68 high-traffic websites with 78 front-end JavaScript libraries. Our approach outperforms existing tools, achieving a 91.76% F1-score in library detection (1.39x higher) and an 82.52% F1-score in version identification with inclusion match (1.38x higher).