J-BusinessDirectory - VCard function

Where can I find the control for VCard function?

In my directory, only logged-in users can view contact information. Presently, in public viewing, clicking on the VCard will download the contact information and generate an email.

I need to have that available for ONLY logged-in users. 

I only see the option to turn the VCards on or off.

I don't think there is an option to assign this function to a certain user group.

I think the problem you describe is as follows, correct me if I am wrong: 

   - You restrict access to 'logged-in' users; so, why does the VCard provide the user with the business's contact information, if they are not 'logged-in'?

Yes, that's the issue.

So, if I cannot assign this function to a user group, my best action is to turn off 'Show Contact Cards'.

Currently, this functionality is not implemented. You can only turn on/off the feature.