bbPress.org

You mean to just redirect one folder to another?

Pretend your old forum was at http://www.domain.com/phpbb2 and the new one is at http://www.domain.com/bbpress

Delete the phpbb2 folder and in your .htaccess add this:

RewriteRule ^phpbb2(.*)$ http://www.domain.com/bbpress/ [L,R=301]

That will make what’s called a Permanent redirect, and in theory teach site crawlers what’s up. Mind, a 401 is for unauthorized access, which is an odd error to get.