The text of the English dub is somewhat confusing, probably due to nonrecognition of the term "baobhan sith" (especially when rendered by a Japanese speaker). The original script is clearer: Bubbancy took the name Laura from the novel Carmilla (which, like Dracula, may be close to the truth in the history of the Hellsing world), but Integra also addresses her as a baobhan sith. Upon realizing her identity, Integra refers to the baobhan sith as the Countess Karnstein, this of course being another reference to the classic vampire novel, Carmilla.
A baobhan sith is a Scottish folk creature, a female vampire in a green dress and with very pale skin. It is pronounced "baa-van-shee." In the Japanese version of the anime, this got rendered as "Buubanshii", which is part of the source for the confusion on her name.