From version 4.6, Artifactory is a Bower registry and lets you register bower packages through remote and virtual repositories. This means you can retrieve bower packages directly from your private Git repositories.
When creating private remote repositories, the Registry URL is redundant and can be left as is.
For example, a private Stash server hosted at http://stash.mycompany.com:7990 with a project named "artifactory" will be registered as follows:
bower register artifactory ssh://git@stash.mycompany.com:7999/artifactory/artifactory.git
Once the server is registered, to download a Bower package from the stash server and cache it in the remote Bower repository in Artifactory (ready for access by users) you can simply run
bower install artifactory