The question implies that the Roman Catholic Church itself procures Bibles for its members and then distributes them. While there may be some number of Bibles that are procured and distributed this way, either directly by the Vatican or by local dioceses and parishes, I don't believe that the majority of Roman Catholics acquire their personal Bibles in this fashion (I am speaking a bit from experience here).
There is also the matter of what exactly should be considered a "Catholic" Bible. Another answer correctly stated that any "authorized" Catholic publication must have a Nihil Obstat and an Imprimatur, in accordance with Title IV of the Code of Canon Law of the Roman Catholic Church. While Canons 822-824 specify the conditions for all publications in general, Canon 825 sets out special conditions for Bibles:
§1. Books of the sacred scriptures cannot be published unless the Apostolic See or the conference of bishops has approved them. For the publication of their translations into the vernacular, it is also required that they be approved by the same authority and provided with necessary and sufficient annotations.
§2. With the permission of the conference of bishops, Catholic members of the Christian faithful in collaboration with separated brothers and sisters can prepare and publish translations of the sacred scriptures provided with appropriate annotations.
Given the formality specified in the canons, I would have thought a centralized list of approved Bibles would be available, but I hadn't been able to locate one. This explanation, from a director of the United States Conference of Catholic Bishops, addressing the question, "Which Catholic Bibles have been approved by the Vatican?", may explain why:
Any Bible which bears an imprimatur may be used by Catholics for personal study and devotion. While the 1983 Code of Canon Law does include a provision for the Holy See to grant the imprimatur for translations of Scripture, I am unaware of any instance in which it has done so.
In addition to the Holy See, the 1983 Code allows conferences of bishops to grant the imprimatur to Scripture translations, a change from previous practice wherein the bishop of the place where the translation was made or published could grant the imprimatur.
Thus it would seem that not even the Vatican keeps track of all the Catholic Bibles that have been published or who published them. There do seem to be centralized lists of approved translations (like this one, from the U.S. Conference of Catholic Bishops), in keeping with the letter of 825 §1, but no list or lists of publishers or specific ISBN's.
I think the correct answer to your question, assuming you mean Catholic Bibles procured both privately and by the Roman Catholic Church, is that they come from some of the same sources that Protestant Bibles do, as well as some dedicated Catholic publishing houses. The English-language Catholic Bibles sold on Amazon, for example, include offerings from Catholic publishers like Ignatius, St. Benedict, and even from the U.S. Conference of Catholic Bishops itself, but there are also ones published by Oxford, Harper, and Zonderavan.