UPDATE:
I came up with this solution when I was pretty new to web design. Now that I am older and wiser, the answer Liam gave seems to be a better option. See the next top answer; it is a more productive solution.
I worked on a project recently and this example worked perfectly. I am giving you the link below.
First you have to add jQuery mobile:
This adds the touch functionality, and then you just have to make events such as swipe:
<script>
$(document).ready(function() {
$("#myCarousel").swiperight(function() {
$(this).carousel('prev');
});
$("#myCarousel").swipeleft(function() {
$(this).carousel('next');
});
});
</script>
The link is below, where you can find the tutorial I used:
http://lazcreative.com/blog/how-to/how-to-adding-swipe-support-to-bootstraps-carousel/