If it's any help to anyone, the Version 2.0 of the bootstrap datepicker no longer works with the accepted answer.
Here's how I got it working on mine:
$('yourpickerid').datepicker({
format: 'dd/mm/yyyy',
}).on('changeDate', function(e){
$(this).datepicker('hide');
});
See http://bootstrap-datepicker.readthedocs.org/en/latest/events.html#changedate