Conversational AI (e.g., Google Assistant, Amazon Alexa) is nowadays omnipresent in many people's life. To enable many functionalities and benefits (such as convenience, utility, and personalization), conversational AI needs to gather large amounts of users' personal data which raises the issue of privacy concerns. As people nonetheless share personal data with conversational AI, it is important to understand which factors determine disclosure (i.e., privacy concerns and willingness to disclose). One important aspect that seems to heighten disclosure in several contexts is interactivity. However, the conceptualization and operationalization of interactivity has often varied between studies. To overcome this, we aimed to investigate three facets of perceived interactivity simultaneously: (1) active control (i.e., whether users can exert control over exchanged information and interaction), (2) reciprocal interaction (i.e., whether there is a two-way flow of information), and (3) synchronicity (i.e., whether information exchange happens quickly). In two survey studies (N-total = 406), we investigated the association between those interactivity facets and disclosure towards conversational AI. Results indicate that all forms of interactivity are correlated with a higher willingness to disclose and in part also with privacy concerns. However, when considering all facets at once in multiple regression, only reciprocal interaction (but not active control and synchronicity) was related to willingness to disclose and none of the three interactivity facets was significantly associated with privacy concerns. Thus, our findings suggest that reciprocal interaction is (compared to active control and synchronicity) the most relevant interactivity facet to understand people's willingness to disclose towards conversational AI.