We appreciate your deep concern for your student.
Although mikveh is the question presenting itself now, it represents a broader issue facing your student. Love is not the only factor in deciding whom to marry. How much weight should a young woman give to religion in making her decision?
As individual as the answer to this question may be, a teacher can help guide a student to a deeper understanding of what is at stake. We suggest that you raise and discuss the different aspects of this broader question. For example: How does she feel now about her boyfriend's stance toward mitzvot and how does it affect her? What are the practical consequences now of his observing mitzvot as a concession to her as opposed to keeping them out of obligation to HaShem or out of respect for tradition? Would these change with marriage?
A major difference between having a relationship and being married is the level of long-term commitment and the possibility of building a family. What role does religion play in her life now? What role would she like to see it play, i.e., does she have long-term spiritual goals? How does she envision her family, someday, when it comes to religion and mitzvot? What does it mean for a family when religion is a source of conflict? What can it mean for a family when religion is a source of strength?
Taharat hamishpachah is a great example of how challenging it can be to observe mitzvot when married to someone who is less interested, since it is so much of a joint effort. If you are comfortable doing so, sharing some of your own relevant experiences with her could be very helpful.
The reason for immersing in a mikveh is that it is commanded by the Torah. Not observing the clean days is in violation of halachot thousands of years old. Sephardi women, in particular, are renowned for holding on to the observance of taharat hamishpachah through the generations, regardless of whether they define themselves as dati. Taharat hamishpachah is private, so its influence is perhaps less readily visible to their daughters. But when it is observed, intimacy is connected to mitzvot and mikveh puts its stamp on a marriage.
For more information, you could direct your student to "Waters of Eden" or "Total Immersion", two titles we have listed under resources.
Choosing whom to marry is a momentous, often difficult, decision. We pray that your student has the wisdom to work through these issues without taking shortcuts. She has already taken a big step in reaching out to you. She is very fortunate to have such a devoted teacher.