In view of the dynamic and partially observable characteristics of non-cooperative bidding games among generation companies in electricity markets, this paper proposes a bidding strategy approach based on the Soft Actor–Critic (SAC) algorithm. First, on the basis of an intercept-parameterized supply function, an electricity market clearing model is established with the objective of maximizing the long-term profit of GenCos, while considering DC power flow constraints and the formation mechanism of locational marginal prices. The intercept of the supply function is defined as the continuous decision variable of each GenCo. Then, to address the limitations of the traditional Deep Deterministic Policy Gradient (DDPG) algorithm in terms of training stability and exploration capability, the SAC algorithm is employed to construct an independent learning framework for GenCos. The use of a maximum-entropy objective enhances policy exploration and convergence robustness. A state–action–reward mapping mechanism based on profit feedback is designed according to the market clearing results, enabling each GenCo to adaptively update its strategy without explicit communication. Finally, numerical simulations are conducted on the IEEE 3-bus and 30-bus systems. The results demonstrate that the proposed SAC-based independent agent approach can effectively approximate Nash equilibrium bidding strategies, exhibits superior convergence characteristics, and reveals potential tacit collusion behavior in electricity markets under high discount factors.