By default, the control should show on the registration form and on the user edit, but not on the user profile where only the selected value shows.
My first guess is that your Joomla site template attempts to override the HTML output of CB, or does some other incorrect CSS formattings.
Try with the default Joomla template. Does it output correctly with the default Joomla template (protostar) ?
(to change template go to Extensions/Templates/Site, then select by checkmarking "protostar", and click "Default" button above)