I'm in the process of upgrading screeenly to the newest release. While switching from Grunt to Gulp I had some problems binding third-party packages into the Gulp workflow.
Luckily there is a nice and simple way to configure the output directory of Bower. Just add a .bowerrc file to the root of your Laravel Project and insert the following code:

{
    "directory": "resources/vendor"
}

Your Bower packages are now downloaded into the resources/vendor/ directory. That's the place where Laravel Elixir expects your CSS and Javascript files. Now you only have to set a new root directory when using the scripts() and styles() function in your Gulpfile, just like so:

mix.scripts(
    [
        'vendor/package-name/package.js',
        'vendor/antoher-package-name/another-package.js',
        'js/app.js',
    ],
    'public/app.js',
    'resources/'
);

And don't forget to add /resources/vendor to your .gitignore file. You don't want to have those files in your version control.