As far as I am aware with Muse it is very limited and is just a publish all affair and not great for full managements from sites.
Depending on how you built the site to edit content on a BC site just go to the url and /admin and login, go to the home page and make contlent changes as you need to.
I tried using Muse on a recent BC project; as Liam states it is "a publish all affair".
Created an entire site with menus in Muse, then published the site into a BC site.
It appeared to simply use the BC site as FTP space to host the Muse site.
The intelligence of the BC platform, recognised the pages from Muse (and some templates setup from Muse) but with regards to the menus; these didn't translate into a BC menu. They were hard coded into every page after Muse re-codes it for every sitemap change.
The guidelines I found for Muse is that you edit the site entirely in Muse and re-publish it each time.
As soon as you edit the pages/templates in BC you sever the link between the Muse project and BC site.
Republishing will overwrite your BC amends, and vice-versa amends in BC aren't visible in your Muse project.
For my project, I ended up using Muse to simply build the page templates and then added my own BC menus to them.
Created all the individual pages and modules inside BC outside of Muse.