Are you sending out mass mailings (even relatively small ones)? Perhaps Mrs B's account has been blacklisted by your SMTP host?
Are you using any mail filters? Perhaps an errant filter is preventing you from sending out mail.
Have you tried disabling your antivirus software? It is known that some interfer with the function of Outlook Express.
Does Mrs B's email address have a non-alphanumeric character in it (an apostrophe for example - @ and . are OK)?