Nothing written by Rabia survives, and it is not certain that she wrote. What exists is a body of sayings, prayers and stories transmitted by others, first in scattered form and then gathered by later collectors, of whom the most influential is Attar, writing his prose Memorial of the Saints some four centuries after her death.
The result is a figure whose historical outline is thin and whose literary presence is enormous. The standard life has her born poor in Basra, orphaned, sold into slavery, and freed by a master who saw a light around her while she prayed at night. Each of those elements is a recognisable hagiographical motif, and the biography as it stands cannot be treated as a record. What can be said with confidence is that a woman of that name lived in eighth century Basra, that she was regarded as an authority in her own lifetime by men who were themselves regarded as authorities, and that sayings were being attributed to her early.
Her position in the tradition is worth stating plainly for what it settled. Sufi literature, which is otherwise overwhelmingly male, placed a woman at the origin of its central doctrine and did not treat that as requiring explanation or defence. When later writers wanted to argue that sanctity is not a function of sex, they cited her, and the citation was accepted. The atlas holds the figure and the source problem together, because both are part of what she is.