Since 4.7 you can filter the post_password_required function:
function my_admins_dont_need_password( $required ) {
if ( current_user_can( 'manage_options' ) ) {
$required = false;
}
return $required;
}
add_filter( 'post_password_required', 'my_admins_dont_need_password' );
Replace manage_options
with whatever capability you want to use to allow users to skip the password form.