This research focuses on optimizing geothermal reservoir modeling tackling issues related to non-uniqueness, subsurface uncertainties, and computational intensity. The proposed workflow integrates Bayesian Particle Swarm Optimization (PSO) and a Bidirectional Gated Recurrent Unit (BiGRU) network to enhance the efficiency of history matching in the context of geothermal resource development under uncertainties. The methodology involves four key steps: firstly, identifying crucial uncertainty parameters such as injection rates and reservoir temperature; secondly, constructing the BiGRU network to capture the nonlinear relationship between these parameters and time series outputs, with Bayesian PSO automating hyper-parameter tuning; thirdly, using Bayesian PSO for the inversion of uncertainty parameters, utilizing the BiGRU as a forward model to reduce computational costs; and finally, conducting a thorough analysis and refinement of errors in predicted responses between the high fidelity model and Bayesian PSO, ensuring the accuracy of the history-matching process. Validation using a 3D fractured geothermal reservoir scenario demonstrates the Bayesian PSO and BiGRU method's efficacy in inverting uncertainty parameters with narrow uncertainties. The Obtained results are compare the performance of predicting the recovery factor (RF) using different surrogate methods, including Gaussian Processes (GP), Radial Basis Function (RBF), and Random Forest Regression (RFR). The proposed Bayesian PSO and GRU-based history-matching approach proves highly accurate and robust for efficiently addressing significant uncertainties in geothermal extraction processes.