Anything DSM-IV-A-or-B-cluster-like I'd call a psychotic disorder personality.

I'd say borderline personality disorder is closest to a BP personality, though BPD would probably be a superset or more severe form of a BP personality.

I'd also say, it's what I believe, that a BP personality makes the underlying BP less severe, possibly masking/preventing it (or the pathogenesis) completely.

But no real thing as in a separate diagnosis. Just as a derivative of BP, making things better and/or worse.

Edit:
BPD also has some SZ personality characteristics: emotional detachment, at times. It used to be called, more specifically, "borderline schizophrenia".