Carbon emissions limit the output demand of traditional fuel-generating units, significantly affecting the electric power and energy balance scheduling mechanisms of modern power systems. To address this, we first analyzed the short-term electric power and energy balance from a dual perspective, along with the electro-carbon coupling mechanism of dynamic dispatching on the source-load side. Based on this analysis, we constructed a framework for low-carbon bilateral demand response (LCBDR). Subsequently, based on the carbon emission flow theory, the carbon emission index information of the demand response system was obtained. Therefore, the short-term electric power and energy balance optimal scheduling model for LCBDR is established to achieve a low-carbon economy. In this study, the enhanced decision tree classifier (EDTC) algorithm is used to predict the electricity consumption behavior of transfer load (TL) user load, and an improved ‘ ε-greedy’ strategy particle swarm optimization (PSO) algorithm is proposed to realize the coordinated optimization of daily operational cost and daily carbon emission of the regional power grid. Finally, by setting up three different perspectives of the simulation examples, the proposed method can effectively realize the regional power grid’s low-carbon, economical, and efficient operation. The feasibility of the model can be verified via the IEEE-30 bus system.