I've encountered similar issues. If there is any sort of proxy firewall, that can play havoc as it doesn't propagate to the bunny. Also, I have found that if docker is installed on the host, it, too, can play havoc with the forwarding (even if not behind a proxy).
I've had to flush the IP tables and rerun the bb.sh to get it to work.
Moreover, when behind a proxy, I've found to get the bunny to work with the Internet, go in and manually reconfigure the bunny's /etc/resolv.conf (where google's DNS may not be accessible behind a firewall). Manually tweaking /etc/apt/apt.conf and possibly for good measure /etc/environment with the various proxy/configuration variables in place also helps.
After configured, you'll probably want to undo your changes so you can deploy it as desired.