After some digging around and after asking a few questions on the Coppermine forum, I was able to get bridging to work between Coppermine 1.4.9 and VB 3.6.0 by using the bridging wizard built into Coppermine.
It's REALLY picky about paths, but one you get them figured out, my user group memberships now show up in Coppermine

Start Coppermine and log in as the admin. Go the admin tools section and scroll down to the bridging wizard. Choose VB 3.0, which is kind of counter intuitive. Follow the instructions, making sure you get the paths right. Make sure you check the "Enable Bridging" radio button at the end.
That should work for you as it did for me.