Once you load WordPress in via Composer (using the GitHub WordPress/WordPress mirror and Composer's "package" repository type), you have to solve a few directory path problems. This Composer script solution helps WordPress find your config file kept in your /config/ directory (You can easily change that path in the bin/wp-config-redirect script)

bootstrap.php

<?php

/**
 * Load WordPress
 * 
 */

define('WP_USE_THEMES', true);
require 'vendor/wordpress/wordpress/wp-blog-header.php';

composer.json

{
    "repositories": [
        {
            "type": "package",
            "package": {
                "name": "wordpress/wordpress",
                "version": "3.6",
                "source": {
                    "url": "https://github.com/WordPress/WordPress.git",
                    "type": "git",
                    "reference": "3.6"
                }
            } 
        }
    ],
    "require": {
        "wordpress/wordpress": "3.6"
    },
    "scripts": {
        "post-install-cmd": "bin/wp-config-redirect",
        "post-update-cmd": "bin/wp-config-redirect"
    }
}

index.php

<?php

require dirname(__DIR__) . '/bootstrap.php';

wp-config-redirect.sh

#!/usr/bin/env bash

########################################################################
# Solves a problem with WordPress being kept in the Composer-managed
# vendor directory, where it looks for wp-config.php only one level
# up from the wp directory. After composer install/update, we run this
# command to create a dummy wp-config.php file that includes our real
# config file, managed in the /config directory (duh).
########################################################################

echo "<?php require dirname(dirname(__DIR__)) . '/config/wordpress.php';'" > "vendor/wordpress/wp-config.php"

So far, the only other thing we've had to do to make this work is:

$ cd public
$ ln -s ../vendor/wordpress/wordpress/wp-admin wp-admin

Just a small typo:

echo "<?php require dirname(dirname(__DIR__)) . '/config/wordpress.php';'" > "vendor/wordpress/wp-config.php"

should be:

echo "<?php require dirname(dirname(__DIR__)) . '/config/wordpress.php';" > "vendor/wordpress/wp-config.php"

Also:

$ cd public
$ ln -s ../vendor/wordpress/wordpress/wp-login.php wp-login.php
$ ln -s ../vendor/wordpress/wordpress/wp-includes wp-includes