Bitcoin prices exhibit high volatility and complex non-linear patterns, making accurate price predictions challenging in the context of cryptocurrency market research. In this study, an optimized SVR-PSO predictive modeling approach is developed to help predict Bitcoin prices, and its performance is compared against a Grid Search-optimized SVR baseline. The SVR-PSO modeling approach developed in this study uses daily historical Bitcoin records obtained from Yahoo Finance between March 10, 2019, and May 11, 2026. The data consists of open, high, low, close, and volume values as attributes, and the closed value as the target. Data preprocessing consists of chronologically organizing the data, removing blank rows, min-max scaling, and splitting the data into 80:20 for training and testing. PSO is used to identify the optimal SVR parameters C, ε, and γ with the aim of reducing MAPE. The optimal parameters for the SVR model are C = 501, ε = 0.001, and γ = 0.001. On the test dataset, the SVR-PSO model achieved an MAE of 1,521.47, an RMSE of 2,101.70, a MAPE of 1.65%, and an R² of 0.9813, outperforming the SVR-GridSearch baseline (MAE 1,559.87; RMSE 2,128.52; MAPE 1.69%; R² 0.9809). These results suggest that SVR-based Bitcoin price prediction is more accurate when optimized using PSO than using a discrete Grid Search.