Effective mentorship is a key factor for driving success in completing a doctoral program or achieving tenure in the professoriate. The effectiveness of a mentor-leader in engaging and empowering mentees depends on the mentor's ability to influence desired attitudinal or performance character changes. This takes place through relational connections for interaction of values, attitudes, behaviors, and principles that are nurtured, constructed, and practiced, building and supporting a mentee-mentor cultural bridge to achieve the desired goal. The mentor and mentee enter the relationship with unique identities and self-cultures that must be transformed, and boundaries crossed in the mentorship process. Such a mentorship cultural bridge is designed to relationally connect mentor and mentee to each other in functional and impactful ways, with goals to discover more about each other's culture, build relational trust and empathy, practice relationship building, improve cross-cultural communication skills, and provide a pathway to improved understanding and valuing of differences. Moreover, this cultural bridge should make graduate education mentorship a mutually beneficial effort and inspire mentees to be successful in a competitive culture of high expectations, such as preparation for and success in a Ph.D. program or mentoring a junior faculty member toward making tenure. This paper introduces a mentorship cultural bridge within the framework of Relational Mentorship Model (RMM), with a focus on the strategies and acts of effective menteeship and mentorship for increasing the success of engineering doctoral students, especially those from under-represented groups, in a research intensive setting. The key tools provided in RMM include: strategies for developing effective mentoring relationships for the general growth of the mentee; understanding the critical characteristics of followership or Menteeship and how relational mentor-leader can be transformational in positively inspiring growth and higher independent performance skills on mentees toward desired success; and developing mutual trust to jointly cross the mentorship cultural bridge in a transformational mentorship process. Holistically, the paper explores how mentorship empowers participants for further success and growth on both professional and personal levels, inside and outside of higher education. An extensive discussion of research evidence on the barriers minority students face in graduate school, challenges majority faculty face in cross-racial and gender mentorships, and suggestions on how to address the identified barriers, make this exploration applicable for any faculty or graduate students who desire to maximize the opportunities from relational mentorship.