Not sure how much you know, so to start at the beginning - you will need to put it in a web page (e.g. html) or javascript file.
Inside the web page you will need a script section:
<script type="text/javascript">
</script>
Inside the script you will need to specify the method in jquery (I prefer mouseenter, see here). Something like (updated from your jsfiddle):
$(document).ready(function () {
var bouncetime = 1700;
var ballheight = 280;
var ballsize = 20;
$('#my_img').animate({'bottom':20}, bouncetime, 'easeInQuad', function() {
$('#my_img').animate({'bottom':70}, bouncetime, 'easeOutQuad', function() {
});
});
$( '#my_img' ).mouseenter( function ()
{
$(this).css('visibility','hidden');
} )
});
Depending on exactly what you want, you could replace the .css(..) with .hide().
You didn't specify it, but to show the image again when the mouse leaves the image, you would do something like (or use hover with two functions rather than mouseenter,mouseleeave see here):
$( '#my_img' ).mouseleave( function ()
{
$(this).css('visibility','visible');
} )