Removing the contact search on a contribution page
I have a fully working donation page set up in civicrm where:


there is a Financial Type "Donations" set up in
Administer/civicontribute/financial type.
Financial Type is set up in the relevant Contribution Page as "Donations".
A Profile is attached to the contribution page that collects
information in fields such as first name, last name and email
address


The settings in the profile are set to 'Used For' standalone form or directory.  'Search views' are switched off.  Advance settings include "Wordpress User account required".

I assume that you have a log in facility set up in the CMS Wordpress and that you have switched on 'Anyone can register' in Wordpress/Settings/General.  When a user completes your form, they should then get registered in both Wordpress and CiviCRM.

You may be seeing the Search Bar only because you are personally logged in as Admin.  Try looking at the contribution page when not logged in and see what shows.

Hope this helps!