This is hard to say. We tend to get around 100,000 downloads for each new version of Bugzilla, but we have no idea how many of those are complete downloads, how many of them result in working Bugzilla installations, etc.
However, Bugzilla has an auto-update feature which retrieves a file from one of our servers, approximately once a week, provided that a Bugzilla administrator has logged in that week. This was introduced in Bugzilla 3.0, but it wasn't working properly until 3.0.4.
In October 2008 we had 55,998 hits on the update file. Since Bugzilla installations check it roughly once per week, divide that number by 4 and it comes out to probably 14,000 Bugzilla installations that are using version 3.0.4 or higher (which is when this feature started to work).
I'd estimate the average number of users for a Bugzilla at around 200, with the major open-source installations having tens of thousands of users, and the smaller corporate installations having around 20-100. That gives us roughly 2,800,000 Bugzilla users around the planet, counting only Bugzilla installations that are version 3.0.4 and higher, have not disabled the update check, have an administrator who regularly logs in, and are not in an environment where they can't access the update file (which is actually fairly common in locked-down corporate environments).