For “anyone” to use it, a pull request will be needed for the core parts library repository, to add a company_name.fzb file with (optionally) an associated png icon files. See files in fritzing-parts/bins/more for samples.
For your own use, to create a bin for your self, the “Parts” window has a dropdown menu with an option to create a new bin. That bin can be exported. The exported bin could be published in the forum (or elsewhere) for anyone to download and import. To work, the parts in the bin also need to exist either in the core parts library, or loaded from fzpz files.
So the parts need to be created, added to a bin file, and either published or merged into the core parts. See downloading the Fritzing library from github and links from there for how AdaFruit has done it.
Not all of the company specific parts need to be in the fzb file. Parts in the same family can be used by adding any one of them to a sketch, then using inspector to switch to other parts in the same family. Assuming the parts have matching properties with different values.