Right off the cuff, I would do the following until you have it installed correctly:
$bb->WP_BB = true;
require_once( 'public_html/wp-blog-header.php' );
2) Change to false:
$bb->mod_rewrite = false;
Once you have bbPress installed and integrated with wordpress (logins), then play around with the permalinks and the including bbPRess functions with WP.