How blutui staging site works is the site you develop. Until published your site is just in staging.
What to do with staging site
Bluid your blutui site. The [your-site].blutui.com is the staging link. This is where you will see your site develop when pushing code up.
To show someone that you dont want admin access to the site send them your site staging link [your-site].blutui.com and the Password that is located in the Security tab of your site.
What happens after publishing.
The staging site still is there. This allows you to chane the code in an area without pushing to live build. This is great to add and test new page layouts.
Just make sure after you make these changes on staging and are happy with them Republish the site to set them live.