How to load shortcode sooner

I am trying to add a shortcode to my menu, the menu item shows up but not the shortcode output.

I think the problem is that the shortcode runs after the menu has run and therefore the shortcode output is not present.

Is there a way to load shortcode sooner?

Thanks

Edit:

Sorry here it is:

//--Nav Menu
function add_profile_link_to_nav(){ 
 if ( is_user_logged_in() ) { ?> 

<ul> 
  <li class="menu-item"id="one"> <a href="http://example.com/members/">All  Members</a>
    <ul class="sub-menu"> 
          <li class="menu-item"><?php echo custom_execute_shortcode(); ?> </li>
    </ul> 
 </li>
</ul>    <!--end menu--->
<?php } 
}
add_action( "wp_nav_items","add_profile_link_to_nav" );

function custom_execute_shortcode() {
 $myfunction= '[bc_user_groups amount="20"]';
 $myfunction_parsed = do_shortcode($myfunction);
 return $myfunction_parsed;
}

Edit:
Hello Ralf912, thanks for the response, I am trying to use your suggestion and I am getting this error code: php_code_error:1:/hsphere/local/home/c262876/mydevelepmentsites.com/maol_bp/wp-content/themes/CC-Child-Theme/functions.php:72:Call to undefined function do_bc_user_groups()
Message:A fatal code error occurred.
I have:

//--Nav Menu
function profile_link_to_nav(){ 
 if ( is_user_logged_in() ) { ?> 

 <ul> 
   <li class="menu-item"id="one"> <a href="http://example.com/members/">All  Members</a>
 <ul class="sub-menu"> 
     <li class="menu-item"><?php echo custom_execute_shortcode(); ?> </li>
 </ul> 
   </li>
 </ul>    <!--end menu--->
<?php } 
}
add_action( "bp_menu","profile_link_to_nav",1 );

function custom_execute_shortcode() {
$atts = array( 'amount' => 20 );
$myfunction_parsed =bc_user_groups( $atts );
return $myfunction_parsed;
}

Thanks

$myfunction= '[bc_user_groups amount="20"]';
$myfunction_parsed = do_shortcode($myfunction);

became

$atts = array( 'amount' => 20 );
$myfunction_parsed = bc_user_groups( $atts );

Call the shortcode function (I asume your shortcode function name is ‘bc_user_groups’) direct.