Bootstrap datepicker hide after selection

You can use event changedate() to keep track of when the date is changed together with datepicker('hide') method to hide the datepicker after making selection:

$('yourpickerid').on('changeDate', function(ev){
    $(this).datepicker('hide');
});

Demo

UPDATE

This was the bug with autoclose: true. This bug was fixed in latest master. SEE THE COMMIT. Get the latest code from GitHub