Not sure how to approach this via javascript, but this code works if you create a class, set up the remote site, and call it using the code at the bottom - so you could pass a URL into this class, and get back the string in the controller...

I would probably rework the XML read method to use the DOM functionality, and I typically store the login/api credentials somewhere else (e.g. a custom setting) but I tried this in my dev org, and it works fine...

global class bitly {

Public String mode;
Public String sUrl;

public String getbitly () {
String shorten;
XmlStreamReader reader;
HttpResponse res;

//First, build the http request
   Http h = new Http();
   HttpRequest req = buildWebServiceRequest(sURL);
   
   //Second, invoke web service call 
   if (mode=='live') {   res = invokeWebService(h, req);   }
     
   if (mode=='live') {    reader = res.getXmlStreamReader();     }
   else
   {
   String str = '<bitly><results shortUrl="http://bit.ly/QqHEm">Foo bar</results></bitly>';
   reader = new XmlStreamReader(str);
   }
   return readXMLResponse(reader,'shortUrl');
  
}


public static HttpRequest buildWebServiceRequest(String purl){
String endpoint;
            HttpRequest req = new HttpRequest();
            endpoint = 'http://api.bit.ly/shorten?version=2.0.1&format=xml&history=1&longUrl=' + purl + '&login=tseth&apiKey=R_948fa681da46221f969e83b2ba52d31e';
            req.setEndpoint(endpoint); 
            req.setMethod('GET');
            return req;
}

public static HttpResponse invokeWebService(Http h, HttpRequest req){
     
     //Invoke Web Service
     HttpResponse res = h.send(req);
     return res;
}


public static String readXMLResponse(XmlStreamReader reader, String sxmltag){
string retValue;
    // Read through the XML
    system.debug(reader.toString());
    while(reader.hasNext()) {
            if (reader.getEventType() == XmlTag.START_ELEMENT) {
                           if (reader.getLocalName() == sxmltag) {
                              reader.next();
                                  if (reader.getEventType() == XmlTag.characters) {
                                           retValue = reader.getText();    
      }
      }
      }
      reader.next();
    }
return retValue;
}

        
}

bitly b = new bitly();
b.mode = 'live';
b.sUrl = 'http://www.bridgefarmconsulting.com';

system.debug('Check BitLy' + b.getbitly() );