Conflict detection plays a crucial role in ensuring flight safety and efficiency and is a critical component of an air traffic control system. Despite the availability of tools to support air traffic controllers in identifying potential conflicts, their quality, and accuracy remain limited due to the challenge of accurately accounting for uncertainty when predicting flight trajectories. To tackle this issue, researchers have explored various studies focused on using probabilistic techniques to model aircraft dynamics and trajectory uncertainty. However, these approaches share several common shortcomings, including their assumptions about uncertainty distributions and the high computational costs of detecting and calculating the risk of conflicts. In response to these challenges, we propose a data-driven approach combining a multi-output generative model with a Bayesian Optimization algorithm to effectively model the uncertainty of aircraft trajectories and rapidly identify the probability of a conflict. Our approach employs the Heteroscedastic Gaussian Process to capture complex trajectory patterns and uncertainty from historical data directly. The proposed predictive model can effectively capture heteroscedastic noise from real data, leading to improved predictions. It achieves Kullback-Leibler divergence around 1 to 1.3 for all dimensions which reduces by >45% for latitude, >24% for longitude, and 4% for altitude compared to the classical homoscedastic GP approach. The method also boasts high-performance predictions for 4D trajectories including descending, climbing, and en-route phases. To pinpoint when two aircraft are most likely to experience a conflict, the Bayesian Optimization algorithm is adopted, which shows good performance in terms of computational efficiency and flexibility for probabilistic conflict detection. The proposed model achieves percentage error <0.25% in estimating the conflict probability with computational cost <14s. By addressing the challenges of uncertainty and computational complexity, our method demonstrates great potential to enhance flight safety and efficiency.