try this:

function my_setup_nav() {
    global $bp;

    // this cause errors if your not logged-in.
    // $bp->bp_nav[\'conversations\'] = false;

    // use this instead:
    unset($bp->bp_nav[\'conversations\']);
}

add_action( \'bp_setup_nav\', \'my_setup_nav\', 1000 );