With a correctly done 301 redirect, as you've noticed, the referred will be the original referer, not the directed URL (foo.example in your example).
You should be able to see the 301 redirects to bar.example in the log files for your foo.example site.
If for some reason you can see the log files for your foo.example web server, then you could track them using Google Analytics.
In the 301 redirect, add campaign tracking variables to the bar.example URL you are redirecting to, including foo (or whatever you fancy) as the campaign or source. Note that this will, of course, overwrite any earlier source attribution.
Make sure though that bar.example has canonical URLs in the head of it's pages, to avoid any problems of duplicate content.
