The Paul Scherrer Institute (PSI) currently delivers the most intense continuous muon beam in the world with up to several 10⁸μ⁺/s and aims at maintaining its leadership by upgrading its beamlines within the High Intensity Muon Beams project (HIMB) (Eichler et al. 2022; Dal Maso et al. 2023) with projected intensities up to 10¹⁰μ⁺/s, and having a huge impact on low-energy, high-precision muon based searches. To reach such high quality tunes during commissioning, a novel tuning strategy is required, due to the large aberrations introduced by the employment of solenoidal elements along the HIMB beamlines. This paper presents the preliminary tests carried out in December 2023 at the Compact Muon Beam Line (CMBL) at PSI, serving the Mu3e experiment (Arndt et al., 1012) a tuning of low energy muon transfer lines with Bayesian algorithms was performed.