The criteria for when the field is displays is on the edit form when creating or editing the form. Currently you can only control it based on the appearance of other fields on the bug, not by the user viewing it.
In Bugzilla 4.0 and newer there is an extension hook that can be used to control whether a custom field is displayed or not. You could create an extension and use that hook to check the user's group membership and display it nor not based on that. See http://www.bugzilla.org/docs/ and pick the [api] link next to the version of Bugzilla you're using. Look for Bugzilla::Extension for information about how to make an extension. There's a section for Template Hooks. The template where those fields are displayed is bug/edit.html.tmpl and the hook name is 'custom_field', so you would create a template in your extension named hook/bug/edit-custom_field.html.tmpl . In that template you can check if the user is in the correct group or not, and set field.hidden = 1 to hide the field.