To address the issue of inaccurate reliability assessment in Full-Scale Structural Tests (FSST) under high-load conditions due to a limited sample size, a reliability assessment method integrating a surrogate model with Bayesian theory is proposed. First, based on the historical test data, the Stacking ensemble surrogate model is used to construct a prior model of the applied load distribution, and the applied load uncertainty is quantified through Bayesian theory. Then, combined with the field test data, the Stacking ensemble surrogate model is used to construct the constraint points load error prediction model, and the uncertainty of the constraint points load error is quantified through Monte Carlo simulation. Finally, the Copula function is used to achieve the reliability assessment of FSST with multiple constraint points load error failures. To enhance the predictive accuracy of the model, an Improved Slime Mould Algorithm (ISMA), which incorporates a good point set and adaptive Cauchy-Gaussian variation strategy, is introduced to optimize the parameters of the Stacking integrated surrogate model synchronously, and an Improved Slime Mould Algorithm optimized Stacking ensemble modeling method (ISMA-Stacking) is proposed. The proposed method is applied to a certain type of FSST reliability assessment case, and the results show that compared with other methods, the Mean Absolute Error (MAE) of the applied load standard deviation prediction model and constraint points load error prediction models under 90% and 100% loading levels are reduced by 42.90%, 50.87% and 54.29%, respectively, and the accuracy of the reliability assessment under the 90% and 100% loading levels are as high as 99.87% and 99.77%, respectively. Therefore, the proposed method can provide theoretical and technical support for the reliability assessment of FSST.