The right way of publishing to BC is using the 'Publish' button on Muse. However, you can also upload once exported the site via Muse as HTML and then follow the document here User manual to upload the files to your BC site.
But this way is not recommended for the sites having webforms created in Muse as the code may break if not published using 'Publish' button.
Also check this Publish your site to Adobe Web Hosting | Adobe Muse CC tutorials
Hope that helps!