Yes, using a Git repository (or a different version control system) would be a sane way to deal with this.
There are several locations bundles are stored in as mentioned in the 'Locating Bundles' section of the documentation. If you customize a bundle the changes will be stored in the following path:
~/Library/Application Support/Avian/Bundles
What appear to be bundle files are just regular directories, you can just 'cd' into them from the shell and start a repo. The bundles in this location only have the deltas from the original bundle in them. So no need to worry about updating the original bundles etc.
Hope this helps!