We propose a Bayesian generative approach, Bayesian Similarity-weighted Aggregation (SimAgg), for combining model weights from federated collaborators in brain lesion segmentation. This method effectively adapts to data variability and incorporates probabilistic modeling to handle uncertainty, enhancing robustness in federated learning (FL). Using a novel multi-armed bandit setup, it dynamically selects collaborators to improve aggregation quality. Simulation results on multi-parametric MRI data show that Bayesian SimAgg achieves high Dice scores across tumor regions and converges approximately twice as fast as non-Bayesian methods, providing an effective framework for federated brain tumor segmentation.