Undergraduate education in the U.S. is racially/ethnically stratified, and there is limited mobility for Black and Latinx BS recipients in STEM majors into the PhD programs from which faculty hiring disproportionately occurs. Bridge programs are proliferating as a means of increasing minoritized students' enrollment in STEM graduate programs, but little social science examines mechanisms of their impact or how impacts depend on the graduate programs to which students seek access. This sequential mixed-methods study of the Cal-Bridge program analyzed trust networks and mechanisms of relational trust as factors in graduate school application, admissions, and enrollment decisions. First, using social network analysis, we examined patterns in the graduate programs to which seven cohorts of Cal-Bridge scholars applied, were admitted, and chose to enroll. Then, we conducted an in-depth case study of the organization in the Cal-Bridge network with the highest centrality: University of California, Irvine's physics and astronomy PhD program. We find the positive admission and enrollment outcomes at UC Irvine were due to intentional, institutional change at multiple organizational levels. Change efforts complemented the activities of the Cal-Bridge program, creating conditions that cultivated lived experiences of mutual, relational trust between bridge scholars and their faculty advisors and mentors. Findings illustrate mechanisms and antecedents of trust in the transition to graduate education. We use these findings to propose a framework that may inform the design of future research and practical efforts to account for the role of trust in inequities and creating more equitable cultures in STEM.