This can be handled more easily than the above answers indicate. You can do this with a single line of javascript in your show handler:
$('.tooltip').not(this).hide();
Here’s a complete example. Change ‘element’ to match your selector.
$(element).on('show.bs.tooltip', function() {
// Only one tooltip should ever be open at a time
$('.tooltip').not(this).hide();
});
The same technique is suggested for closing popovers in this SO thread:
How can I close a Twitter Bootstrap popover with a click from anywhere (else) on the page?