Bipolar is a mood disorder and borderline is a personality disorder so yes, you can have both. Just like you can also have an anxiety disorder or PTSD. They are different types of disorders.
Edit to say: I can elaborate more, in a science-y way, if you want me to...
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Diagnoses:
PTSD with Dissociative Symptoms, Borderline Personality Disorder, Generalized Anxiety Disorder, Fibromyalgia and Chronic Pain
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