mail() function and Bcc field

[Alhazred]

I need to send the same email in plain text format to several users.
I can do that, but there is a problem: those users who use a gmail account (and only them) can see the email addresses in the Bcc field.

Is there a way to hide those addresses to gmail users?

This is my code

$i=0;
while($row = mysql_fetch_array($addresses)) {
    if($i==0) //first addres into the field To:
        $receiver = $row['email'];
    else //others into Bcc
        $bcc .= $row['email'].", ";
    $i++;
}

$header .= "MIME-Version: 1.0\r\n";
$header .= "Content-type: text; charset=iso-8859-1\r\n";
$header .= "From: My site <[email protected]> \r\n";
$header .= "Bcc: ".$bcc."\r\n";
$object = "email's object";
$message = "email's text.\r\n";
mail($receiver, $object, $message, $header);