Remote data querying for Twitter Bootstrap 2.0 Typeahead without modifications, this fork adds the functionality of getting the clicked item's value

remote-typeahead.js

<script>
// Charles Lawrence - Feb 16, 2012. Free to use and modify. Please attribute back to @geuis if you find this useful
// Twitter Bootstrap Typeahead doesn't support remote data querying. This is an expected feature in the future. In the meantime, others have submitted patches to the core bootstrap component that allow it. 
// The following will allow remote autocompletes *without* modifying any officially released core code. 
// If others find ways to improve this, please share.
//User clicked some value by Adrian Hove
    var autocomplete = $('#searchinput').typeahead()
        .on('keyup', function(ev){

            //User clicked some value
			 $('ul.typeahead li').on('click', function(){
                                        alert($(this).html().replace(/<(?:.|\n)*?>/gm, '')); //Or your function
			            	});
            ev.stopPropagation();
            ev.preventDefault();

            //filter out up/down, tab, enter, and escape keys
            if( $.inArray(ev.keyCode,[40,38,9,13,27]) === -1 ){

                var self = $(this);
                
                //set typeahead source to empty
                self.data('typeahead').source = [];

                //active used so we aren't triggering duplicate keyup events
                if( !self.data('active') && self.val().length > 0){

                    self.data('active', true);

                    //Do data request. Insert your own API logic here.
                    $.getJSON("http://search.twitter.com/search.json?callback=?",{
                        q: $(this).val()
                    }, function(data) {

                        //set this to true when your callback executes
                        self.data('active',true);

                        //Filter out your own parameters. Populate them into an array, since this is what typeahead's source requires
                        var arr = [],
                            i=data.results.length;
                        while(i--){
                            arr[i] = data.results[i].text
                        }

                        //set your results into the typehead's source 
                        self.data('typeahead').source = arr;

                        //trigger keyup on the typeahead to make it search
                        self.trigger('keyup');

                        //All done, set to false to prepare for the next remote query.
                        self.data('active', false);
                       
                    });

                }
            }
        });
</script>

<input type="text" id="searchinput" data-provide="typeahead">

Docs from the jQuery site:

Rewriting the .live() method in terms of its successors is straightforward; these are templates for equivalent calls for all three event attachment methods:

$(selector).live(events, data, handler); // jQuery 1.3+
$(document).delegate(selector, events, data, handler); // jQuery 1.4.3+
$(document).on(events, selector, data, handler); // jQuery 1.7+
The events argument can either be a space-separated list of event type names and optional namespaces, or an event-map of event names strings and handlers. The data argument is optional and can be omitted. For example, the following three method calls are functionally equivalent (but see below for more effective and performant ways to attach delegated event handlers):

$("a.offsite").live("click", function(){ alert("Goodbye!"); }); // jQuery 1.3+
$(document).delegate("a.offsite", "click", function(){ alert("Goodbye!"); }); // jQuery 1.4.3+
$(document).on("click", "a.offsite", function(){ alert("Goodbye!"); });

So you should try:

$(document).on('click', 'ul.typeahead li'', function(){});

Basically the way .live worked was by listening for the defined events on the common parent DOM node for the dynamic nodes being modified. The version I shared listens on the document and uses "ul.typeahead li" as the context.