Narcissists also have mood instability. Many disorders are comorbid with other disorders. These disorders are not anything like regular diseases, psychiatric disorders are merely collections of symptoms. It is surprisingly rare for a person to only have one mental health disorder . There is a lot of overlap in all disorders, especially personality disorders. Mood instability and irritability are common in all mental health disorders. Most people with a personality disorder also have mood disorders and people rarely seek treatment for personality disorders alone, they go for treatment when other symptoms are bothering them such anxiety or depression.
Based on my research BPD has a better prognosis for recovery, Bipolar is a life-long disorder with a constant need for "maintenance" medication. Such medications are not required for BPD although usually urged by most psychiatrists, because that's what psychiatrists do: prescribe medicine.

The reason why it would appear bipolar has a better prognosis on the surface is because its easier to treat: here take this cocktail of drugs and your symptoms will get better. It takes more work on behalf of mental health professionals to treat personality disordered people. So not that many in the field are willing to undertake this daunting task as it requires good old fashioned hard work, no amount of pills will make it just go away.