How to add smooth scrolling to Bootstrap's scroll spy function

Do you really need that plugin? You can just animate the scrollTop property:

$("#nav ul li a[href^='#']").on('click', function(e) {

   // prevent default anchor click behavior
   e.preventDefault();

   // store hash
   var hash = this.hash;

   // animate
   $('html, body').animate({
       scrollTop: $(hash).offset().top
     }, 300, function(){

       // when done, add hash to url
       // (default click behaviour)
       window.location.hash = hash;
     });

});

fiddle

If you have a fixed navbar, you'll need something like this.

Taking from the best of the above answers and comments...

$(".bs-js-navbar-scrollspy li a[href^='#']").on('click', function(event) {
  var target = this.hash;

  event.preventDefault();

  var navOffset = $('#navbar').height();

  return $('html, body').animate({
    scrollTop: $(this.hash).offset().top - navOffset
  }, 300, function() {
    return window.history.pushState(null, null, target);
  });
});

First, in order to prevent the "undefined" error, store the hash to a variable, target, before calling preventDefault(), and later reference that stored value instead, as mentioned by pupadupa.

Next. You cannot use window.location.hash = target because it sets the url and the location simultaneously rather than separately. You will end up having the location at the beginning of the element whose id matches the href... but covered by your fixed top navbar.

In order to get around this, you set your scrollTop value to the vertical scroll location value of the target minus the height of your fixed navbar. Directly targeting that value maintains smooth scrolling, instead of adding an adjustment afterwards, and getting unprofessional-looking jitters.

You will notice the url doesn't change. To set this, use return window.history.pushState(null, null, target); instead, to manually add the url to the history stack.

Done!

Other notes:

1) using the .on method is the latest (as of Jan 2015) jquery method that is better than .bind or .live, or even .click for reasons I'll leave to you to find out.

2) the navOffset value can be within the function or outside, but you will probably want it outside, as you may very well reference that vertical space for other functions / DOM manipulations. But I left it inside to make it neatly into one function.

$("#YOUR-BUTTON").on('click', function(e) {
   e.preventDefault();
   $('html, body').animate({
        scrollTop: $("#YOUR-TARGET").offset().top
     }, 300);
});