Mongoose update of embedded document

I'm slowly going mad trying to understand how to update the value of an embedded document in mongoose, and written some node.js code which demonstrates the problem.

var mongoose = require('mongoose');
var Schema = mongoose.Schema;

mongoose.connect('mongodb://localhost/mongoose_broken');

var ASchema = new Schema({
   value : { type: String, index: { unique: true } },
   bs    : [BSchema],
});
var BSchema = new Schema({
   value : { type: String },
});
var A = mongoose.model('A', ASchema);
var B = mongoose.model('B', BSchema);

// Add an entry of A, with 1 embedded B
//
var a = new A();
a.value = "hello";
var b = new B();
b.value = "world";
a.bs.push(b);

a.save(function(err) {
   if (err) {
      console.log("Error occured during first save() " + err);
      return;
   }

   // Now update a by changing a value inside the embedded b
   //
   A.findOne({ value: 'hello' }, function(err, doc) {
      if (err) { console.log("Error occured during find() " + err); return; }

      doc.bs[0].value = "moon";

      doc.save(function(err) {
         if (err) console.log("Error occuring during second save()");

         // Check b was updated?
         //
         if (doc.bs[0].value != "moon") {
            console.log ("b was not updated! (first check)");   
         } else {
            console.log ("b looks like it was updated (first check)");

            // Do a fresh find
            //
            A.findOne({value: "hello"}, function(err, doc_2) {
               if (err) { console.log("Error occured during second find() " + err); return; }

               if (doc_2.bs[0].value != "moon") {
                  console.log ("b was not updated! (second check)");   
               } else {
                  console.log ("b looks like it was updated (second check)");
               }
            });
         }
      });
   });
});

Output from running this is:

b looks like it was updated (first check)
b was not updated! (second check)

Any idea why the update of the embedded document is not saved?