Bootstrap’s tooltip doesn’t disappear after button click & mouseleave

This is because trigger is not set. The default value for trigger is 'hover focus', thus the tooltip stay visible after a button is clicked, until another button is clicked, because the button is focused.

So all you have to do is to define trigger as 'hover' only. Below the same example you have linked to without persisting tooltips after a button is clicked :

$('[data-toggle="tooltip"]').tooltip({
    trigger : 'hover'
})  

the doc example in a fiddle -> http://jsfiddle.net/vdzvvg6o/