As one of the primary contributors to carbon emissions, road transportation systems are expected to be included in carbon emission management frameworks in the near future. Demand-Responsive Transit (DRT) will face a new constraint: carbon emission costs. Currently, no widely established framework exists for carbon emission management in transportation systems. Carbon tax and carbon trading are two commonly implemented carbon regulatory policies worldwide, and both are expected to be extended to the transportation sector. However, the effectiveness of these policies in incentivizing carbon reductions in DRT systems and the potential challenges they may pose remain uncertain. To fill this gap, this paper developed route planning models for the Open Capacitated Low-carbon Vehicle Routing Problem (OCLCVRP) and designed a series of experiments using standard benchmark instances to explore the impacts of carbon tax and carbon trading policies on the operation of DRT systems. The results indicate that although both carbon tax and carbon trading policies are effective in reducing carbon emissions, they lead to the loss of a fundamental attribute of DRT systems—service equity. As carbon prices rise, this loss of equity becomes more pronounced, ultimately increasing the failure rate of DRT systems and undermining the effectiveness of carbon emission regulatory policies. To mitigate this issue, this paper proposed a dynamic carbon quota-based carbon trading scheme. Through a case study, the proposed dynamic carbon quota proves to be effective for the public transportation sector in reducing carbon emissions while ensuring service equity under the carbon trading scheme.