From the source
/**
* Template tag for breadcrumbs.
*
* @param string $before What to show before the breadcrum
* @param string $after What to show after the breadcrumb.
* @param bool $display Whether to display the breadcrumb (true) or return it (false).
* @return string
*/
You want to do:
$breadcrumbs = yoast_breadcrumb('<p class="breadcrumbs_p">','</p>', false);
or do the following and not echo.
yoast_breadcrumb('<p class="breadcrumbs_p">','</p>');