As the next generation of turbomachinery components becomes more sensitive to instrumentation intrusiveness, a reduction of the number of measurement devices required for the evaluation of performance is a possible and cost-effective way to mitigate the arising of non-mastered experimental errors. A hybrid methodology that couples experimental techniques with modeling techniques through a Bayesian data-driven framework is employed to reduce the instrumentation effort. A numerical model is employed to provide an initial belief of the flow, which is then updated based on undersampled experimental observations by a Bayesian inference algorithm. The goal of the present work is to showcase the proposed hybrid methodology and demonstrate its partial application through Gaussian Process regression in reducing the instrumentation effort and testing time at the outlet of a low aspect ratio axial compressor stage representative of the last stage of a high-pressure compressor. Preliminary results show an accurate reconstruction of the mean flow field with a direct uncertainty quantification provided by the Bayesian approach.