This is not possible. The BigBlueButton server must be accessible to the client's users for them to login to a BigBlueButton session. When logged in, they will see the URL for your BigBlueButton server in the address bar.
You could try hiding the BigBlueButton in an iFrame, but this doesn't work consistently across browsers (search through these forums for previous posts related to iFrame for more information).
Also, even with the iFrame approach, a user could use the built-in browser console to watch the network traffic and any files loaded from the BigBlueButton server would be visible.
Regards,.. Fred