Headers can be tricky and are a common pitfall for spam filters if you are sending from an address that is different to the default site one. It should look a little bit like this however:
$headers = 'From: Edd <[email protected]>;' . "\r\n";
$headers .= 'Bcc: Admin <[email protected]>;' . "\r\n";
wp_mail($to, $subject, $message, $headers);
