Bugzilla shows that I am properly logged in on the bugzilla front-page (http://bugzilla.redhat.com/bugzilla), yet when you go to query bugs or submit a new bug, it loses the fact that you are logged in.
Bugzilla uses cookies for authentification purposes so you need to make sure you have them enabled in your browser. Have you done that?
Cookies were enabled and I had cookies for bugzilla in my Netscape cookie cache. Some of them referred to various different roots on the server, so I've just taken the cookies out of the cookies file and relogged in which appears to have cured the problem. It's possible that I got a weird cookie in there right after the switch to bugzilla.redhat.com (when I had to access via IP), so I'll close this bug and reopen it if I notice further problems.
Sorry bout that. The paths have been changed recently regarding the cookies that get set which may cause some issues with people with older cookies. Relogging in usually fixes this but leaves the older stale cookies. Laying around. Let me know if it happens again.