To address the imperfect bidding mechanisms for independent energy storage as an emerging market participant in competitive joint electricity markets, the bidding behavior of various market entities by modeling power quantities and price offers is simulated. Based on this, a bi-level optimization model is constructed to represent the bidding strategy of independent energy storage participating in the day-ahead energy and reserve joint market. In the upper level, the independent energy storage system maximizes its revenue in the dayahead energy and reserve joint market by optimizing its power-price bidding strategy. In the lower level, the power trading center clears the market by minimizing the total social electricity procurement cost. To improve the computational efficiency of the model, the lower-level problem is reformulated using the KKT conditions and the strong duality theorem. Simulation studies are conducted using a commercial solver to verify the effectiveness of the proposed bidding strategy in optimizing independent energy storage participation and enhancing its performance in the market.