Accurate short-term photovoltaic (PV) power forecasting is crucial for ensuring the stability and efficiency of modern power systems, particularly given the intermittent and nonlinear characteristics of solar energy. This study proposes a novel hybrid forecasting model that integrates complete ensemble empirical mode decomposition with adaptive noise (CEEMDAN), the jellyfish search (JS) optimization algorithm, and a bidirectional long short-term memory (BiLSTM) neural network. First, the original PV power signal was decomposed into intrinsic mode functions using a modified CEEMDAN method to better capture the complex nonlinear features. Subsequently, the fast Fourier transform and improved Pearson correlation coefficient (IPCC) were applied to identify and merge similar-frequency intrinsic mode functions, forming new composite components. Each reconstructed component was then forecasted individually using a BiLSTM model, whose parameters were optimized by the JS algorithm. Finally, the predicted components were aggregated to generate the final forecast output. Experimental results on real-world PV datasets demonstrate that the proposed CEEMDAN-JS-BiLSTM model achieves an $R^2$ of 0.9785, a MAPE of 8.1231%, and an RMSE of 37.2833, outperforming several commonly used forecasting models by a substantial margin in prediction accuracy. This highlights its effectiveness as a promising solution for intelligent PV power management.