Beatrice is a rogue witch. She can use sorceries, but is apparently not of the Vinheim Dragon School. Judging from her catalyst's description, she's probably from a clan of witches. The flow of time in Lordran is distorted, and after helping the Chosen Undead fight the Four Kings, she tries to fight them herself and dies in the attempt. This is evidenced by her corpse appearing in the Valley of Drakes after the Four Kings are defeated.
Contrasts with Vinheim catalysts. This ancient catalyst shows signs of being used for age-old sorceries. It has passed the hands of many generations to get here.
Also, she wears the Witch Set, which bears the description:
Almost all magic users that employ a wand studied at Dragon School, but Beatrice is one of the few exceptions. She braved the Abyss but did not live to tell of her ordeal.