Hello! Even though this outside my immediate area of expertise, as a public librarian (I'm a man though), I feel like I would be more than willing to answer this question. First, it is worth recognizing that when "public" libraries first started, most notably being Ben Franklin's lending library in Pennsylvania in 1731, the profession of 'librarian' did not exist yet. More importantly, the idea of libraries being free was also completely foreign. Here, at the earliest libraries, people paid fees for a membership and often times fees per book use. This allowed some people in the general public to access knowledge that otherwise would have been out of their range due to cost. Men typically worked in these libraries. However, the "free" library system that we know today is a product of much later thinking, and it was here that women began to work at in greater numbers and for a variety of reasons.

Public libraries began to take hold in American throughout the 19th century -- with many having fees for membership being mandatory. By the last quarter of the 19th century, some library systems began reshaping into a much more inclusive atmosphere. Enoch Pratt Free Library in Baltimore is a great example of how libraries changed over time. Here, the city of Baltimore was gifted over $1,000,000 by Enoch Pratt to open four public libraries that would (as inferred in the title) be free. He described his gift by saying:

"My library, shall be for all, rich and poor without distinction of race or color, who, when properly accredited, can take out the books if they will handle them carefully and return them."

It was a pretty radical idea for the time. It was men were who predominantly worked in the branches initially. This is especially true for large library systems in New England, where library positions were heavily dominated by elite men. However, during the 19th century, women from elite libraries started volunteering at libraries, most notably to work with children.

When the American Library Association was founded in 1876, which is still the governing body over library programs across the country, it's initial membership numbers show how overwhelmingly men were in the field, with 90 being men and 30 being women. This did change starting at the turn of the century. By 1904, a librarian named Mary Cutler Fairchild conducted research and saw that women heavily outnumbered men who held positions in libraries, however they had very little administrative responsibilities. This would change a bit over the next half century. Women continued to lack being the administrators, but it was women who taught and trained librarians through college programs and it was these women who greatly influence and created the models for library services (like reference, cataloguing, and collection development). Here's a great description of what happened during this period:

At the turn of the twentieth century, library education was seen as a good career path for primarily white, middle- and working-class women who could either not afford or did not want to go to college. It also attracted women as a second career when teaching was not a good fit. Some women continued their education after college with library school because it offered them a more focused and usable curriculum. Among the career paths available to women at this time, librarianship appealed to many because the training was relatively short, the career path offered public service and, as the nation expanded westward, potential opportunities for adventure.

The middle of the 20th century also saw a shift of where professional women who were librarians began earning their spot in administrations across the country. For example, in 1951, Amy Winslow became the first woman to be Director of the Pratt Library, one of the most influential library systems in American history. This trend continued throughout the 20th century.

Please let me know if this answered your question and if you have any follow-ups.