我也遇到了同样的问题，终于得到了解决方案！
我只是一个Jquery的初学者，所以我相信你可以清理这一点。而且，可能最好使用你自己的Caroal结构，并只使用2类的标题，你想动画。
诀窍是使用Animate.css，但你必须禁用Firefox的动画字幕上的Ease功能，否则会导致问题。
在此处拨弄：http://jsfiddle.net/z6xq12bh/4/
有关更多动画效果：http://daneden.github.io/animate.css/
于飞：

<div id="carousel-example-generic" class="carousel slide" data-ride="carousel">
      <!-- Indicators -->
      <ol class="carousel-indicators">
        <li data-target="#carousel-example-generic" data-slide-to="0" class="active"></li>
        <li data-target="#carousel-example-generic" data-slide-to="1"></li>
        <li data-target="#carousel-example-generic" data-slide-to="2"></li>
      </ol>

      <!-- Wrapper for slides -->
      <div class="carousel-inner">
        <div class="item active">
          <img src="http://placehold.it/1200x400" alt="...">
          <div class="carousel-caption">
              <h3 class="toggleHeading">Caption Text</h3>
              <p class="toggleCaption">This is some text<p>
          </div>
        </div>
        <div class="item">
          <img src="http://placehold.it/1200x400" alt="...">
          <div class="carousel-caption">
              <h3 class="toggleHeading">Caption Text 2</h3>
               <p class="toggleCaption">This is some text<p>
          </div>
        </div>
        <div class="item">
          <img src="http://placehold.it/1200x400" alt="...">
          <div class="carousel-caption">
              <h3 class="toggleHeading">Caption Text 3</h3>
               <p class="toggleCaption">This is some text<p>
          </div>
        </div>
      </div>

      <!-- Controls -->
      <a class="left carousel-control" href="#carousel-example-generic" role="button" data-slide="prev">
        <span class="glyphicon glyphicon-chevron-left"></span>
      </a>
      <a class="right carousel-control" href="#carousel-example-generic" role="button" data-slide="next">
        <span class="glyphicon glyphicon-chevron-right"></span>
      </a>
    </div> <!-- Carousel -->

JS：

<script>
    var carouselContainer = $('.carousel');
    var slideInterval = 5000;

        function toggleH(){
            $('.toggleHeading').hide()
            var caption = carouselContainer.find('.active').find('.toggleHeading').addClass('animated fadeInRight').one('webkitAnimationEnd mozAnimationEnd MSAnimationEnd oanimationend animationend',
                function (){
                $(this).removeClass('animated fadeInRight')});
        caption.slideToggle();
        }

        function toggleC(){
            $('.toggleCaption').hide()
            var caption = carouselContainer.find('.active').find('.toggleCaption').addClass('animated fadeInUp').one('webkitAnimationEnd mozAnimationEnd MSAnimationEnd oanimationend animationend',
                function (){
                $(this).removeClass('animated fadeInUp')
        });
        caption.slideToggle();
        }
    carouselContainer.carousel({
    interval: slideInterval, cycle: true, pause: "hover"})
    .on('slide.bs.carousel slid.bs.carousel', toggleH).trigger('slide.bs.carousel')
    .on('slide.bs.carousel slid.bs.carousel', toggleC).trigger('slide.bs.carousel');
     </script>

CSS：

.toggleHeading {
        animation-delay: 0.5s;
      -webkit-animation-delay: 0.5s;
         -moz-animation-delay: 0.5s;
           -o-animation-delay: 0.5s;
           -moz-transition: none !important;
    }

    .toggleCaption {
        animation-delay: 1.5s;
      -webkit-animation-delay: 1.5s;
         -moz-animation-delay: 1.5s;
           -o-animation-delay: 1.5s;
           -moz-transition: none !important;
    }