Probabilistic data association (PDA) improves semantic SLAM in perceptually aliased scenes, but existing methods often assume a fixed landmark set, recompute association weights as the map grows, or rely on hand-tuned null-hypothesis weights. To address these limitations, we propose \textbf{BPDA-GMM}, an online Bayesian PDA framework for semantic SLAM with a growing object-level map. BPDA-GMM uses a Dirichlet-process prior to induce a Chinese Restaurant Process (CRP) association model, where accumulated evidence favors existing landmarks, and the concentration parameter assigns probability mass to new landmarks. For each semantic detection, plausible candidates are selected by a joint semantic-geometric gate, CRP-weighted association probabilities are computed, and object landmarks are updated as semantic Gaussians in closed form. The resulting landmark set forms a Gaussian mixture model, and its dominant component is passed to the back-end as a max-mixture semantic factor. When association weights are inconclusive, an ambiguity-triggered $α$-divergence tempering step improves discrimination. Finally, a decoupled back-end zeroes the pose Jacobian of semantic factors, allowing noisy detections to refine landmarks without directly perturbing the trajectory. Experiments in simulation and on a real indoor dataset demonstrate improved trajectory accuracy, semantic mapping quality, and robustness to perceptual aliasing and classifier errors over state-of-the-art baselines. Code and video are publicly available at https://github.com/thanhnguyencanh/BPDA-SLAM.