laoding bloginfo url in function array?

I'm using wp customizer in a theme and I want to load a page using a link in admin bar. Link in admin bar is added, and link format is like this: http://www.domain.com/dashboard/customize.php?url=/page_to_edit

However, it still loads the homepage in the customizer iframe, so guess I'm doing something wrong. For reference, This is the code I'm using (the part that matters):

$admin_bar->add_menu( array(
        'id'    => 'my_page',
        'parent' => 'customize_page',
        'title' => 'My Page',
        'href' => admin_url( 'customize.php?url=/my_page/'),
        'meta'  => array(
            'title' => __('My Page'),
            'target' => '_self',
            'class' => 'my_menu_item_class'
        ),

Now, if I load the full absolute URL it works fine, but no idea how to make bloginfo load inside this array. I found in another post that I can use get_bloginfo (not sure if that's correct) but also no idea how to make it work after the admin_url part.

Any help really appreciated, this is driving me crazy!