Why not make assigning bugs work sort of like FlaggedRevs -- as a new user, you can make changes, but the changes won't take effect until they're reviewed and approved? After a bureaucrat sees that you're behaving responsibly, or after you've made a certain number of changes that have been approved, then your changes are automatically approved.
With that system, you don't have to make a request of any particular person; it's whoever is the first to see that there are changes that need to be reviewed.