There are six types of music libraries: (1) those developed to support research and performance departments of music in larger university or college settings; (2) those developed to support conservatories; (3) those housed within public libraries; (4) those developed as independent research libraries; and (5) special libraries supporting agencies such as National Public Library. The Music Library Association has information on music librarianship, including job postings.  Music libraries (more properly known as production music libraries) that license their copyrighted music for use in film, television and radio production.
Most production music libraries (especially those in the UK), own all rights (bundled) and license the product at affordable rates. Some 'buyout libraries' are only licensing the mechanical rights and performance rights are still owned by the library.
 See also
Notable UK production music libraries:
KPM De Wolfe Bruton