Looking for specific template tags for BP?
https://codex.buddypress.org/developer/developer-docs/template-tag-reference/
Other than that, I’ll offer a couple suggestions:
First, why not keep the default WP toolbar on the front side with the following snippet in mu-plugins? That way your “My SItes” menu is always on – front and back. All kinds of tips and tricks for customizing the toolbar after that.
add_filter( 'show_admin_bar', '__return_true' , 1000 );
Second, using only WP functions I offer you this link to a users primary blog or the dashboard if they do not have a site:
<?
$user_id = get_current_user_id();
$active = get_active_blog_for_user( $user_id );
if ( $active )
$url = get_home_url( $active->blog_id );
else
$url = get_dashboard_url( $user_id );
echo '<a href="'.$url.'">'.$url.'</a>';
?>