Basic setup is to put the JSX templates into their own repo; bring that in with your choice of package manager; and each project requires them like any other package code. There are a lot of tutorials out there on setting up a UI/component library so I won't reinvent them here ;)
The main thing you will need to work out is how to make the shared package available, assuming you're not open sourcing it:
"dependencies": {
"yourcomponents": "git+ssh://git@bitbucket.org/account/repo.git#1.2.3"
}
...main thing to note about that approach is all your builds will need SSH access as well, so they can access the repo. Also, we found NPM was quite slow pulling from private git repos; and didn't put much feedback onto the screen (worst case was someone on a slow connection getting no Terminal feedback for 10mins). We actually found Bower worked better, but since it's deprecated I wouldn't go there at this point.