I understand that you are having a difficult time understanding your girlfriend’s behavior, even though you are studying to be a clinical psychologist. This is understandable since eating disorders are very complex and something in which psychologists specialize. If you have never experienced a person with an eating disorder or studied them, your girlfriend is feeling pain, both physically and mentally. It will take a lot of work by her to overcome bulimia during treatment.
It sounds to me that she knows you recognize her symptoms. You should not ignore her behavior, but try to talk about it to her in a supportive manner while expressing your concern about her health. Mentioning her weight will only provide a point to argue about. If she will talk to you, listen carefully and try to make her aware of counseling available in your area. Show your concern and offer to accompany her to treatment. Understanding how much you support her may motivate her to get help.
You say that your girlfriend is experiencing kidney problems. You don’t say if that is reduced urine flow, pain on urination, or that she is retaining fluid in her tissues due to reduced kidney function. She should be under the care of a medical doctor and perhaps that will open the door to getting psychological help.
If your girlfriend is bingeing and purging, then she has bulimia. If she is also having difficulty eating and has reduced her food intake, then she may also have anorexia. Eating disorders require a team approach. The treatment protocol is a two-fold approach. Psychotherapy is necessary to help her deal with the underlying issues. Nutrition therapy will help her understand she needs to nourish her body and help her develop more normal healthy eating patterns. With both of these treatments working together and the earlier treatment is sought, the more likely she will reduce the bulimic behavior.
I do understand that you have a background in psychology, but it may be better if she seeks the help of a psychologist or psychiatrist with experience in treating eating disorders, as well as a Registered Dietitian. Your emotional connection to her may interfere with your ability to work with her on a professional level. She will definitely need your support and understanding during her recovery.