Normally the Bootstrap dropdown doesn't scroll so I assume you have changed the CSS to make the .dropdown
scroll using overflow-x
and setting a specific height.
If so, you can do something like this..
$('#year-picker').on('shown.bs.dropdown', function () {
var ele = $(this).find("li>a:contains('2009')");
var posi = ele.offset().top-ele.innerHeight();
$('.dropdown-menu').animate({
scrollTop: posi
}, 1000);
})