I've actually been working on a WordPress bridge myself, it essentially works but needs a little more tidying up before I'll pop it on the net.
Essentially there are a few problems I've had to solve.
1) You need to include WordPress's wp-config.php, but this file also attempts to load the entire WordPress libraries, which you do not want. Why? Because WordPress uses some of the same functions as Coppermine which means you get a lovely page full of "function redeclared" errors.
Fix?
In wp-config.php we have this line which loads the main WordPress code base:
if ( !defined('ABSPATH') ) define('ABSPATH', dirname(__FILE__) . '/');
So, all we do is define ABSPATH before including wp-config.php to point to an empty "wp-settings.php" file and huzzah! We've got the WordPress configuration settings without conflicting code.
2) Now we haven't loaded WordPress..... how on Earth do we authenticate?!?!
I had previously written a function to manually do this myself, but I recently found somebody else had the same idea, but they wrote it much neater and smarter than myself:
https://gist.github.com/1026786Small WPAuth class allows you to verify a wordpress cookie is correct and to return the user ID.
3) Group management isn't quite so simple in WordPress, you can either code it to use group management from a plugin like Simple:Forum or you can rewrite a fair chunk of the udb_base to use the WordPress roles system (which would probably be a smarter idea).
Anyway, I haven't finished working on my bridge, I'm not sure if it will ever actually be all that flexible since it's coded pretty tightly for me own server.
But, I thought I would share my discoveries, that should significantly aid anybody trying to do this (and please chip in thoughts if you think of better solutions).