The resilience of urban drainage systems (UDS) is increasingly recognized as a critical component in sustainable urban infrastructure, particularly under accelerating urbanization and climate change. Existing resilience assessment methods often rely on static, system-wide overflow metrics, overlooking spatiotemporal variability and component-level performance. This can mask critical vulnerabilities such as pipe surcharging, a major contributor to basement flooding. This study introduces a novel Bottom-Up System Resilience Assessment (BUSRA) framework that quantifies dynamic resilience at the pipe level using hydraulic performance metrics, rather than system overflow alone. BUSRA computes time-resolved cumulative resilience trajectories for each pipe and aggregates them into minimum, final, and system-level indicators, linking local behaviour to network-scale performance. BUSRA is applicable to single-event and continuous rainfall scenarios and to separate or combined sewer systems. The framework was applied to an urban drainage system in Kitchener, Ontario, Canada. Its system-level indicators were benchmarked against the Global Resilience Analysis method for consistency, while BUSRA provides additional component-level and temporal insights beyond what global metrics capture. Key findings include: (1) resilience should be treated as dynamic, as temporally aggregated metrics overestimate system performance; (2) spatial aggregation obscures localized vulnerabilities, whereas BUSRA reveals component-specific weaknesses; and (3) absence of surface flooding does not guarantee resilience, as internal surcharging can still cause significant damage. By delivering time-series and map-based diagnostics at multiple scales, BUSRA enables targeted practical interventions, such as pipe upsizing, storage, and Low Impact Development deployment, and supports adaptive, risk-informed infrastructure planning.