Modern pop culture sure has latched onto the image of the monk as scribe. And that's not terrible--monasteries (and women's convents, although you'd be harder pressed to find cartoons and ad campaigns based on that) were one of the most important centers of both education and book production throughout the Latin Middle Ages. But they definitely weren't alone.

Throughout the medieval period, their partner in crime, so to speak, were the royal and princely courts. This includes the papal and episcopal households. Although scholars don't tend to talk about "bureaucracy" until the later twelfth or even thirteenth century for most of the West, the textualization of early medieval governance and political culture runs far deeper than we used to think. Now, it's true that most of these scribes would still have been religious--our word "clerk" comes from cleric! The difference is that many of them would have been in the hierarchy of priests outside monastic and mendicant orders--some ordained priests, but many more in what's called "minor orders" (deacons etc).

That will be especially true as the twelfth century gives way to the thirteenth and a new context for book copying and creation develops: the universities. Men in orders of course play major roles in university academic life and conflict (Thomas Aquinas, Bonaventure, Duns Scotus, etc), but in addition to being at war with each other for funding and control, the Franciscans and Dominicans (and sometime Benedictines) are fighting with "secular" priests and deacons (that is, those who live 'in the world', saeculum or "age", instead of "religious", who follow a religio or monastic Rule). Once again, clerks form a major class of book producers.

Along with the universities comes the rise of cities, probably both connected to the burgeoning economies. And thus we get another stratum of scribes--some of whom still have nominal priestly status as deacons or whatnot; some of whom are avowedly laymen and women. (Yes, we know of women professional scribes--Christian and Jewish!) They do a lot of ad hoc work with business and legal affairs, city record-keeping, and so forth, but some of them are also copying books and producing luxury manuscripts just like monastic houses.