How can I insert a dynamic URL in my email template?

I have no experience with this plugin, but it looks like you can add extra template variables with a filter named 'wpbe_tags':

    function template_vars_replacement( $template ) {
        $to_replace = array(
            'blog_url'         => get_option('siteurl'),
            'home_url'         => get_option('home'),
            'blog_name'        => get_option('blogname'),
            'blog_description' => get_option('blogdescription'),
            'admin_email'      => get_option('admin_email'),
            'date'             => date_i18n(get_option('date_format')),
            'time'             => date_i18n(get_option('time_format'))
        );
        $to_replace = apply_filters('wpbe_tags', $to_replace);

        foreach ( $to_replace as $tag => $var ) {
            $template = str_replace( '%' . $tag . '%', $var, $template );
        }

        return $template;
    }

So, this might do the trick:

add_filter( 'wpbe_tags', 'wpse_99484_extra_tpl_var' );

function wpse_99484_extra_tpl_var( $to_replace )
{
    $to_replace['username'] = function_to_get_buddy_press_user();
    return $to_replace:
}

I am not sure what the correct function_to_get_buddy_press_user() is in your situation, it depends on the context of this email.

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