We study the backward problem of reconstructing the past electrical state of the heart using a simplified bidomain model. This problem is highly ill-posed, and consequently the stability analysis and regularization technique are essentially required. Our main contribution is twofold. First, we establish the conditional stability estimates for the backward problem, focusing on the recovery of the transmembrane potential at a positive past time. Building on this, we further extend the analysis to reconstruct the initial state of the biotissue, which is more challenging due to more weak stability. These stability results are derived by using Carleman estimates for the governed system coupled by parabolic and elliptic equations. Second, based on the established stability results, we propose a minimization-based numerical approach involving a penalty term to solve the inverse problem and validate the theoretical results through numerical experiments. The reconstructions demonstrate the effectiveness of the proposed method and provide the numerical verifications of the stability estimates.