Rosabeth was a student of the Melfian Academy, where she studied pyromancy under Master Glocken. Pyromancy was something she was good at, but she was not satisfied with this because of her adoration for Master Carhillion of the Fold, another teacher at the Academy who taught sorcery. She once heard him giving a lecture on Drangleic, the Melfian Academies and sorcery, and became fascinated with him and his teachings. When she tried to learn sorcery she was woefully inept (probably didn't have the intelligence) and realized it was not for her.
At the Academy she was training at, she was being taught by Pyromancer Glocken, an academic infamous for creating the Quartz rings (which afforded him a hefty profit). It seems she was a very promising pupil. Rosabeth explains that Pyromancer Glocken did not like that Carhillion thought the Academies were terrible places to be taught, which makes sense as Pyromancer Glocken was making a fortune by selling his Quartz rings to eager students too lazy to study.
When Carhillion left for Drangleic, Rosabeth followed him. During her travels she bumped into Carhillion once or twice. From these encounters Carhillion may have indicated that he would teach her sorcery if she wished, but the pair lost contact. Rosabeth crossed the mountains into Drangleic and was attacked by "frightful things" (likely monsters and brigands) on numerous occasions. Upon reaching Drangleic Rosabeth approached the Shaded Woods. It was there that she was petrified, likely by the Basilisk that waits on the other side of the door.
When the Player frees her from her petrification, she boldly proclaims that she has her very own teacher; Carhillion of the Fold. Though it seems these sentiments were not shared by Carhillion, and upon reaching Majula she decides to "keep at it alone" (it is likely that Carhillion did not believe her teachable and she is just saving face).
Despite her failings as a sorcerer, she is a very promising pyromancer and will happily train the Player as repayment for their help.
When aggroed she attacks the Player with a mixture of pyromancy spells. She mostly uses Fireball, Combustion and Fire Orb.