When I send an email using Bcc to several people, in the email they receive it has my email address in both the From section and the To: section. Am I doing something wrong or is there away to resolve this?

Did you fill in the "To" field? If Outlook has nothing for that field, it may simply use your own email address. I don't think it is a problem you need to solve.

If I put an email address in the To: portion, then this will get included with all the other emails as well. I thought the purpose of Bcc was to be able to send several emails at once to several people without them knowing who else the message was sent to.

Yes, they won't see the recipients in the Bcc field. But Outlook just used your own email address in the "To" field and didn't disclose any emails in the Bcc field.

You don't like Outlook to put your email address in the "To" field? If this is the problem you want to fix, you need to use another email client such as Outlook Express, which uses "Undisclosed-Recipient" if you leave the field "To" blank.