Transformer health index (HI) is a powerful tool for quantifying the overall health of a power transformer, due to the fact that it appraises its condition based on different criteria that are related (often in complex ways) to the long-term degradation factors that cumulatively lead to its end-of-life. Several authors have proposed different approaches to the HI calculation, e.g., analytical expressions, binary logistic regression, fuzzy logic models, support vector machines, and artificial neural networks. This paper proposes using Bayesian "Wide & Deep" machine learning model for the HI calculation, where the wide model part is the Bayesian ordered robust "probit" regression, while the deep part is the Bayesian artificial neural network. Both model parts are trained simultaneously within the Bayesian setting, using the so-called "joint learning" process with a Markov-chain Monte Carlo algorithm. Model is demonstrated using the actual transformer data.