Public displays may adapt intelligently to the social context, tailoring information on the screen, for example, to the profiles of spectators, their gender or based on their mutual proximity. However, such adaptation decisions should on the one hand match user preferences and on the other maintain the user's trust in the system. A wrong decision can negatively influence the user's acceptance of a system, cause frustration and, as a result, make users abandon the system. In this paper, we propose a trust-based mechanism for automatic decision-making, which is based on Bayesian Networks. We present the process of network construction, initialization with empirical data, and validation. The validation demonstrates that the mechanism generates accurate decisions on adaptation which match user preferences and support user trust.