Driven by the green and low-carbon transformation of urban logistics, the integration of crowdsourced delivery and green transportation is considered an important pathway to achieving sustainable last-mile delivery. This study focuses on urban crowdsourced delivery using cargo bikes and develops an extended behavioral model based on the Theory of Planned Behavior (TPB). The model systematically examines the key factors influencing the public’s behavioral intention (BI) to participate as crowdshippers. While retaining the core structure of TPB, the model incorporates external variables—perceived risk (PR), policy support (PS), and infrastructure conditions (IC)—to improve its explanatory power and applicability to real-world delivery scenarios. A questionnaire survey was conducted in South Korea, yielding 600 valid responses. The results indicate that usage attitude and perceived behavioral control exert significant positive effects on BI. PR has a significant negative effect on both attitude and BI. PS indirectly enhances BI by improving attitudes, whereas IC primarily influences BI by strengthening the public’s sense of control. This study not only expands the theoretical explanatory power of the TPB model in the context of green crowdsourced delivery but also provides empirical evidence for policymakers and platform operators.