Transparency is an important aspect of human-robot interaction (HRI), as it can improve system trust and usability leading to improved communication and performance. However, most transparency models focus only on the amount of information given to users. In this paper, we propose a bidirectional transparency model, termed a transparency-based action (TBA) model, which in addition to providing transparency information (robot-to-human), allows the robot to take actions based on transparency information received from the human (robot-of-human and human-to-robot). We implemented a three-level (High, Medium and Low) TBA model on a robotic system trainer in two pilot studies (with students as participants) to examine its impact on acceptance and HRI. Based on the pilot studies results, the Medium TBA level was not included in the main experiment, which was conducted with older adults (aged 75-85). In that experiment, two TBA levels were compared: Low (basic information including only robot-to-human transparency) and High (including additional information relating to predicted outcomes with robot-of-human and human-to-robot transparency). The results revealed a significant difference between the two TBA levels of the model in terms of perceived usefulness, ease of use, and attitude. The High TBA level resulted in improved user acceptance and was preferred by the users.