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Robust position reconstruction is paramount for enabling discoveries in astroparticle physics as backgrounds are significantly reduced by only considering interactions within the fiducial volume. In this work, we present for the first time a method for position reconstruction using a Bayesian network which provides per interaction uncertainties. We demonstrate the utility of this method with simulated data based on the XENONnT detector design, a dual-phase xenon time-projection chamber, as a proof-of-concept. The network structure includes variables representing the 2D position of the interaction within the detector, the number of electrons entering the gaseous phase, and the hits measured by each sensor in the top array of the detector. The precision of the position reconstruction (difference between the true and expectation value of position) is comparable to the state-of-the-art methods -- an RMS of 0.69 cm, ~0.09 of the sensor spacing, for the inner part of the detector (<60 cm) and 0.98 cm, ~0.12 of the sensor spacing, near the wall of the detector (>60 cm). More importantly, the uncertainty of each interaction position was directly computed, which is not possible with other reconstruction methods. The method found a median 3-$\sigma$ confidence region of 11 cm$^2$ for the inner part of the detector and 21 cm$^2$ near the wall of the detector. We found the Bayesian network framework to be well suited to the problem of position reconstruction. The performance of this proof-of-concept, even with several simplifying assumptions, shows that this is a promising method for providing per interaction uncertainty, which can be extended to energy reconstruction and signal classification., Comment: 16 pages, 22 figures