The quickly growing popularity of AI companions poses risks to mental health, personal wellbeing, and social relationships. Past work has identified many individual factors that can drive human-companion interaction, but we know little about how these factors interact and evolve over time. In Study 1, we surveyed AI companion users (N = 303) to map the psychological pathway from users' mental models of the agent to parasocial experiences, social interaction, and the psychological impact of AI companions. Participants' responses foregrounded multiple interconnected variables (agency, parasocial interaction, and engagement) that shape AI companionship. In Study 2, we conducted a longitudinal study with a subset of participants (N = 110) using a new generic chatbot. Participants' perceptions of the generic chatbot significantly converged to perceptions of their own companions by Week 3. These results suggest a longitudinal model of AI companionship development and demonstrate an empirical method to study human-AI companionship.