Ensuring that predictions of machine learning (ML) classification models are accompanied by uncertainty estimates is one of the main pillars of trustworthy AI. Current research in uncertainty quantification focuses mainly on epistemic uncertainty of the ML model, but rarely takes account of input measurement uncertainty, which is vital for traceability in metrology. In this work we propose a Bayesian framework for generative ML classification models that takes account of input measurement uncertainty. We take the specific case of a Bayesian quadratic discriminant analysis (BQDA) model, and apply it to metrological land cover datasets from Copernicus Sentinel-2 from 2020 and 2021. We benchmark the performance of the model against more popular classification models used in land cover maps such as random forests and neural networks. To validate and assess the generalisability of such a model, we also run simulations over synthetic classification data, varying distribution type and strength of the input measurement noise. We find for both real and synthetic data, the BQDA model presented is more trustworthy, in the sense that it is more interpretable, explicitly models the input measurement uncertainty, and maintains predictive performance of class probability outputs across datasets over different domains and sizes, whilst also being more computationally efficient.