The progress bar doesn’t display in real-time on Windows or Mac for Webdav connections (which this is). The connection is browser-independent – that has no bearing once Windows has mounted the device as a drive-letter, or Mac has it mounted in Finder.
It sounds as though you are accessing the My Book Live over a Relay connection instead of using Direct Connect. You’ll need to go into the Dashboard, check under “Remote Access” near the top. If it says it’s using a Port Forwarding or Direct Connection, you’re using the fastest access method, and something else is causing the slowness. If it says Relay, it’s routing through our servers first before hitting the remote location. Check our KBA#8526 for more on how to setup Port Forwarding.