Ah-ha!  A cookie problem–while I’d set the cookie domain for WordPress to allow subdomains to work, bbPress didn’t know about WordPress’s cookie settings, so bbPress didn’t set the right cookie domain.  Worse, this meant that the cookie didn’t quite match up to what WordPress expected, so logging out in WordPress tried to blank a cookie that wasn’t set, not the login cookie set by bbPress.  The fix is to add something like

$bb->cookiedomain = '.yoursite.com';

to bb-config.php (that is, match what you’ve set in WordPress). Not the most obvious way to set an option, but it works.