I have a very simple XPage with a table and some input fields. The application uses the bootstrapv3.0.0 theme and the OpenNtf bootstrap4Xpages plugin released on 2014-01-28.
Are you running IE11 in compatibility mode? Try turning off compatibility mode and see if the site loads.
By default intranet sites load in compatibility mode, which I think really means your web site is going to look awful if it was made in the last 15 years mode.
Per Henrik Lausten has an xSnippet that can display a warning to your users if they are running like so. http://openntf.org/XSnippets.nsf/snippet.xsp?id=display-warning-message-if-internet-explorer-uses-compatibility-view-mode