Good day, BlueFlash.

I do not use bugzilla from 2.x version. Now bugzilla can track the work time?
If so, tst can update it via xml-rpc.
If no, you can use new attribute = "Bugzilla issue key" for tasks. And then make report for them.

I use only JIRA for now, and support it. I do not know bugzilla so well.
If you can spend some time for implementing bugzilla extension for tst it will be great. I can help you to do this.