Ajax text field | hide for visiter if empty ?

Hello,
the AJAX text field is really cool. I know, it is supposed to be a frontend action. And in general a "click here" or some other visual hint is displayed for the owner...
But how do I hide such a field for the visiter, if it is still empty? The owner may not enter some text, or he decides to do it later. Than I have an empty, collapsed bubble graphic. That looks really odd.

EDIT:
Additionally, I tried the CB Privacy plugin. I can see and change the privacy setting, but it has no effect.

Bubble is purely CSS, it displays the same way any field does. You should be able to set CB > Configuration > User Profile to not display empty fields; can't guarantee this will work for the ajax field as it has custom code that is returned. CB Privacy has no affect when you're viewing your own profile or if a moderator is viewing the profile.

Thats why i am asking... the user are simple registered users. I also checked the global empty field setting... it seems not to work for the Ajax field. At the moment I am clueless...

EDIT:
By the way, what is the differencr between the first and last parameter option "discrete" and "hidden" ?

Given custom code is rendered, the field is never empty so the empty parameter probably won't work. Discrete display and hidden display don't have a whole lot of differences. It's mainly a different CSS class to allow better styling. The main difference is hidden changes the background for the input to transparent.