We present, to the authors' knowledge, the first application of Bayesian inference to atmospheric differential optical absorption spectroscopy (DOAS) tomography resulting in a full 3+1D reconstruction of the NO₂ concentration distribution from a long-path (LP) DOAS setup with 22 intersecting measurement paths. Four novel long-path DOAS instruments (HyDOAS) were deployed at the Ludwig-Maximilians-University main campus in Munich, complemented by point measurements from the Air Quality Inspection Box (AIRQUIX) sensor. Reconstructions were performed using the Numerical Information Field Theory for Python (NIFTy) inference framework with a combination of Metric Gaussian Variational Inference (MGVI) and geometric Variational Inference (geoVI), which provide access to the full posterior probability distribution. The reconstruction achieves strong internal consistency (overall reduced chi-squared = 0.518, Pearson correlation > 0.9), and remains consistent with independent point-sensor validation even under a more challenging low-concentration, high-wind scenario (reconstruction referenced chi-squared = 0.842). The method captures small-scale spatial features invisible to conventional point monitoring networks. Key findings reveal that under low-wind conditions, nitrogen dioxide (NO₂) accumulates in building corners and low-ventilation zones, often tens of meters from emission sources, likely due to transport of nitric oxide (NO) from street emitters followed by oxidation and trapping in recirculation zones. Cross-validation against independent point sensor measurements demonstrates agreement within the posterior uncertainty prediction despite challenging low-concentration conditions. These results highlight the value of Bayesian tomographic reconstructions for exposure assessment and suggest that regulatory monitoring networks may not be fully representative for reflecting the actual pollution exposure of the population.