With the rapid advancement of autonomous vehicle (AV) technology, AVs are progressively seen as interactive agents with some level of autonomy, as well as some context-dependent social features. This introduces new challenges and questions, already relevant in other areas of human-robot interaction (HRI) - namely, if an AV is perceived as a social agent by the human with whom it is interacting, how are the various facets of its design and behaviour impacting its human partner? And how can we foster a successful human-agent interaction (HAI) between the AV and the human, maximizing the human's comfort, acceptance, and trust in the AV? In this work, we attempt to understand the various factors that could influence naïve participants' acceptance and trust when interacting with an AV in the role of a driver. Through a large-scale online study, we investigate the effect of the AV's autonomy on the human driver, as well as explore which parameters of the interaction have the highest impact on the user's sense of trust in the AV. Finally, we analyze our preliminary findings from the user study within existing guidelines on Trustworthy HAI/HRI.