The ten Mahavidyas are not a random collection. Read in order they run from Kali, who is the cremation ground and the end of things, to Kamala, who is Lakshmi and the goddess of ordinary prosperity, and the sequence is generally understood as covering the full range of what the Goddess is rather than as a ranking. Bhairavi stands fifth, near the middle, and she is one of the boundary cases that make the list argue with itself.
She is fierce, and so belongs with Kali, Tara and Chhinnamasta at the terrifying end. But her book and rosary place her with learning, and her association with tapas places her with disciplined practice rather than with transgression. Several texts pair her with Bhairava as a consort in an ordinary way that the more independent Mahavidyas do not permit so easily.
Kinsley notes in his study of the ten that the members vary greatly in how much independent tradition they carry: some, Kali and Tara above all, have deep separate histories, while others appear chiefly within the group. Bhairavi sits between those cases. The name itself is very old and attaches to many things, including female tantric practitioners, who are called bhairavis. The goddess as fifth Mahavidya is a narrow and comparatively late specification of a much broader term, and reading the wider usage back into the list is a common and misleading error.