Please confirm if you are facing issue while trying to publish to Business Catalyst?
If yes then this must be a login issue. It might be either firewall or some proxy settings that are not allowing Muse to connect to the Adobe Server , hence you are unable to login and publish to Business Catalyst.
It can happen at the time of launch of Adobe Muse or while publishing to Business Catalyst via Muse as in both the cases it required a login.
Please refer to Zak's post in the link below and let us know if it works.