No need to unbind anything, you can bind another hover to your slider and it works good
$('.start_options').bind({
mouseleave: function () {
var $start = $(this),
startOffset = $start.offset();
$slider = $('.start_options');
$slider.css({
position: 'absolute',
top: startOffset.top,
left: startOffset.left - ($slider.width()) + 10
});
$slider.hide();
},
mouseenter: function (e) {
$slider.show();
}
});