Walker menu not displaying at all

The walker code is okay, but in order to have this markup:

<ul class="nav navbar-nav" data-in="fadeInDown" data-out="fadeOutUp">
    ...
</ul>

..in the array passed to the wp_nav_menu() function, set items_wrap to:

<ul id="%1$s" class="%2$s" data-in="fadeInDown" data-out="fadeOutUp">%3$s</ul>

So the full markup would be:

<div class="collapse navbar-collapse" id="navbar-menu">
<?php 
    wp_nav_menu( array(

        'menu_class' => 'nav navbar-nav',
        'container' => '',
        'depth' => 2,
        'theme_location' => 'main-menu',
        'walker' => new My_BS_Walker_Nav_Menu(),
        'items_wrap' => '<ul id="%1$s" class="%2$s" data-in="fadeInDown" data-out="fadeOutUp">%3$s</ul>',

    ));
?>
</div>

Or you can omit the menu_class parameter and simply add the classes via the items_wrap value:

<div class="collapse navbar-collapse" id="navbar-menu">
<?php 
    wp_nav_menu( array(

        'container' => '',
        'depth' => 2,
        'theme_location' => 'main-menu',
        'walker' => new My_BS_Walker_Nav_Menu(),
        'items_wrap' => '<ul id="%1$s" class="nav navbar-nav" data-in="fadeInDown" data-out="fadeOutUp">%3$s</ul>',

    ));
?>
</div>