Adobe Muse CC allows you to publish your temporary website to Adobe at no charge for a 30-day trial period. This gives you the opportunity to send a live URL to your client for review. All sites in trial mode with Adobe will include the domain, example http://website.businesscatalyst.com. If you decide to take the site "live" by paying for the monthly hosting, you can transfer your own domain and remove the .businesscatalyst.com subdomain. Or you can export the HTML and host the final site with a hosting provider of your choice.
If you have questions about BC, there’s no reason not to reach out to Karim.Ingrid s.