Edit:
As Maximus points out below, the 3.x bootstrap solution is:
$('.navbar-collapse a').click(function(){
$(".navbar-collapse").collapse('hide');
});
https://jsfiddle.net/yohuLuj2/
Old Answer for 2.x bootstrap:
You should be able to do that by adding a click handler to the list items and then closing the nav that way.
$('.nav-collapse').click('li', function() {
$('.nav-collapse').collapse('hide');
});
Heres a jsfiddle:
http://jsfiddle.net/hajpoj/By6ym/4/
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