Send A Message To One Recipient & No Sender Using The MailAddress Class?

How can I send a email message to just once person? When I use the following, I have to put in a valid sender address as well as the recipient address in order for my message to be sent. This will send two messages: One to the sender, and one to the recipient. How can I just have my application just send to the recipient only using the Smtp Client Class?

MailAddress fromAddress = new MailAddress(sender);
MailAddress toAddress = new MailAddress(recipient);
MailMessage message = new MailMessage(fromAddress, toAddress);
SmtpClient mailSender;
mailSender = new SmtpClient("Smtp.test.com", 25);
message.Bcc.Add(fromAddress);
message.Subject = subject;
message.IsBodyHtml = false;
message.Body = body;