Thanks Brenden. It would appear that for when logged in,
CMS/App_Themes/Default/bootstrap.css is used.
When logged out,
CMS/App_Themes/Default/DesignMode.css is used.
This is the cause for the differences. I applied the bootstrap.css stylesheet after all my other stylesheets using
<link href="/Kentico82/CMSPages/GetResource.ashx?stylesheetfile=/Kentico82/App_Themes/Default/bootstrap.css" type="text/css" rel="stylesheet"/> Do you know of any problems with this solution? I don't see anything different besides this webpart now being styled correctly while viewing it logged out.