andrea_r,
What is the goal? Are you trying to to have mu and bbPress share the same user table? bbPress and mu are using different databases (as opposed to different tables in the same database)?
I can help, but I need to know exactly how things are and how you want them to work.
I think this is your situation (apologies if I misunderstood you):
You have mu and bbPress installed and working off of different databases. You want bbPress to store its content in that separate database, but you want it to draw its users from mu's database.
If that is the case, this is what should work. The top of bbPress' config.php should look like:
//These are for the information about the database into which bbPress should store its content
define('BBDB_NAME', 'bbpress');
define('BBDB_USER', 'username');
define('BBDB_PASSWORD', 'password');
define('BBDB_HOST', 'localhost');
// This is the information about mu's database. bbPress will look for users in this database
define('USER_BBDB_NAME', 'mu');
define('USER_BBDB_USER', 'mu username');
define('USER_BBDB_PASSWORD', 'mu password');
define('USER_BBDB_HOST', 'localhost');
// You just told bbPress to use that mu database to look for users, but it doesn't yet know the name of the *table* to use.
// Change 'wp_users' and 'wp_usermeta' to be the table names of mu's user tables.
define('CUSTOM_USER_TABLE', 'wp_users');
define('CUSTOM_USER_META_TABLE', 'wp_usermeta');