I stumbled upon this passage in a speech of Maria M. Stewart, the early 19th century American abolitionist, entitled "What If I Am a Woman?"
In the thirteenth century, a young lady of Bologne devoted herself to the study of the Latin language and of the laws. At the age of 23 she pronounced a funeral oration in Latin in the great church of Bologne; and to be admitted as an orator, she had neither need of indulgence on account of her youth or of her sex. At the age of 26 she took the degree of doctor of laws, and began publicly to expound the Institutes of Justinian. At the age of thirty, her great reputation raised her to a chair, where she taught the law to a prodigious concourse of scholars from all nations. She joined the charms and accomplishments of a woman to all the knowledge of a man. And such was the power of her eloquence, that her beauty was only admired when her tongue was silence.
As far as I can tell, it's more or less a lift from a book called Sketches of the history, genius, disposition, accomplishments, employments, customs and importance of the fair sex, in all parts of the world : interspersed with many singular and entertaining anecdotes.
But the original book doesn't include a name. Does anyone with a more substantial understanding of 13th century Bologne have an educated guess?
Well, the source you refer to is an early modern source, so right off the bat, I'm a bit sceptical that this woman even existed.
I've checked out the source you quote and one of the first pages states the the purpose of the volume is:
To give a brief detail of the hiftory of the Fair Sex - to infpire them with a fenfe of their value and importance - to excite them to laudable pursuits...
All this is followed by references to 'authors consulted', many of whom just seem to be interested parties with myths, legends and accounts of varied veracity to share.
The fact that the original book does not include a name is quite telling. You see, it was a habit of some early modern authors to invent exemplary females from the middle ages in order to promote proto-feminist materials. Many medieval and early modern writers emphasised tradition and lineage as a sort of de facto authority. You can see this in the medieval work of Christine de Pisan.
So, although the first documented woman to graduate with a law degree in Bologna did so in the 18th century (1732), it benefited the author of this history of the "fair sex" to find or invent medieval antecedents.
From what I understand of medieval universities (which, admittedly, is cursory since I work on medieval and early modern Scotland), these were men only zones. Of course, some women did achieve significant instruction in typically male subjects, but this would have been the result of private tutoring or careers as nuns.
Alas, I haven't many specific sources to share on this one, but the following certainly reinforce the maleness of education:
Jordan, William Chester. Europe in the High Middle Ages. 1st American ed. New York: Viking, 2003.
Epstein, Steven. An Economic and Social History of Later Medieval Europe, 1000-1500. Cambridge: Cambridge University Press, 2009.
Lilley, Keith. Urban Life in the Middle Ages, 1000-1450. Basingstoke: Palgrave Macmillan, 2002.
Nicholas, David. The Growth of the Medieval City from Late Antiquity to the Early Fourteenth Century. London: Longman, 1997.
Swanson, R. N. The Twelfth-Century Renaissance. Manchester: Manchester University Press, 1999.
Cushing, Kathleen G. Reform and the Papacy in the Eleventh Century: Spirituality and Social Change. Manchester: Manchester University Press, 2005.
Then as far as women go, you can check:
Bitel, Lisa. Women in Early Medieval Europe, 400-1100. Cambridge: Cambridge University Press, 2002.
Van Houts, Elisabeth. Memory and Gender in Medieval Europe, 900-1200. Toronto: University of Toronto Press, 1999.
Finally, I'm not sure whether her findings have been published widely, but Paula Findlen of Stanford University is working on just this subject and suspects that the unnamed exemplary women of the middle ages who are alleged to have had careers such as that of your quoted material are mostly fictitious.
Sorry to disappoint :(