Ideal solution will be to take QueryUI without tooltip. This will work. In case you don't want to do that please include Bootstrap after JQueryUI. Ensure you have unique components from each (you can custom build both libraries with required components)

Bootstrap has a way to to reset any component like:

var bootstrapButton = $.fn.button.noConflict() // return $.fn.button to previously assigned value

$.fn.bootstrapBtn = bootstrapButton            // give $().bootstrapBtn the Bootstrap functionality

The above code will work when bootstrap is loaded after JQueryUI

Ref: http://getbootstrap.com/javascript/

Here is relevant code from Bootstrap:

  var old = $.fn.tooltip



  $.fn.tooltip = function (option) {

    ....

  }





  $.fn.tooltip.noConflict = function () {

    $.fn.tooltip = old

    return this

  }