In socially assistive robotics, an important research area is the development of adaptation techniques and their effect on human-robot interaction. We present a meta-learning based policy gradient method for addressing the problem of adaptation in human-robot interaction and also investigate its role as a mechanism for trust modelling. By building an escape room scenario in mixed reality with a robot, we test our hypothesis that bi-directional trust can be influenced by different adaptation algorithms. We found that our proposed model increased the perceived trustworthiness of the robot and influenced the dynamics of gaining human's trust. Additionally, participants evaluated that the robot perceived them as more trustworthy during the interactions with the meta-learning based adaptation compared to the previously studied statistical adaptation model.