Boostrap tabs in editor window

I have not, but instead of using the Bootstrap tabs, why not use the bootstrap css and jquery calls and apply it to the OOTB Kentico Tabs Web Part. That way you are using the stock part with all of the functionality and look and feel of the bootstrap one. This is how I implemented it.

I ran into this same problem. I had the issue with tabs, and also dropdowns. It seems Kentico's jquery may interfere with bootstrap, or for some reason bootstrap does not auto-initialise tabs. So I run a piece of javascript on page load to forcibly check them. I hope this helps you.

$(document).ready(function(){
    //check if design mode or edit mode
if($("body").hasClass("DesignMode") || $("body").hasClass("EditMode")){

    //fix tabs
    $('.nav-tabs a').click(function (e) {
      e.preventDefault()
      $(this).tab('show');
    });

    //fix dropdowns
    $('.dropdown-toggle').dropdown();
    }
});