The rise of mobile health (mHealth) technologies has enabled real-time monitoring and intervention for mental health conditions using passively sensed smartphone data. Building on these capabilities, Just-in-Time Adaptive Interventions (JITAIs) seek to deliver personalized support at opportune moments, adapting to users' evolving contexts and needs. Although prior research has examined how context affects user responses to generic notifications and general mHealth messages, relatively little work has explored its influence on engagement with actual mental health interventions. Furthermore, while much of the existing research has focused on detecting when users might benefit from an intervention, less attention has been paid to understanding receptivity, i.e., users' willingness and ability to engage with and act upon the intervention. In this study, we investigate user receptivity through two components: acceptance(acknowledging or engaging with a prompt) and feasibility (ability to act given situational constraints). We conducted a two-week in-the-wild study with 70 students using a custom Android app, LogMe, which collected passive sensor data and active context reports to prompt mental health interventions. The adaptive intervention module was built using Thompson Sampling, a reinforcement learning algorithm. We address four research questions relating smartphone features and self-reported contexts to acceptance and feasibility, and examine whether an adaptive reinforcement learning approach can optimize intervention delivery by maximizing a combined receptivity reward. Our results show that several types of passively sensed data significantly influenced user receptivity to interventions. Our findings contribute insights into the design of context-aware, adaptive interventions that are not only timely but also actionable in real-world settings.