Hide custom post type field from author?

The easiest way to do that would be to check the capabilities with current_user_can before displaying the field.

For instance, the administrator role has the capability manage_options which your newly created users won’t have. So you can do something like this:

<?php
// wherever your fields are...
if(current_user_can('manage_options'))
{
   // display your fields here.
}

Or if you have an entire meta box on the custom post type’s page you don’t want to show, you can check the capabilities before adding it.

<?php
add_action('add_meta_boxes_{YOUR_POST_TYPE}', 'wpse72883_add_box');
function wpse72883_add_box()
{
    if(!current_user_can('manage_options'))
        return; // current user isn't an admin, bail

    // add the meta box here
}

It might also be useful to add your own capability to check rather than use a built in one. To give your administrator role the edit_business_details…

<?php
$role = get_role('administrator');
if($role)
    $role->add_cap('edit_business_details');

That only needs to happen once — on plugin activation for instance.

<?php
// some plugin file.
register_activation_hook(__FILE__, 'wpse72883_activate');
function wpse72883_activate()
{
    $role = get_role('administrator');
    if($role)
        $role->add_cap('edit_business_details');
}

You can then check for that capability just like manage_options.

<?php
// wherever your fields are...
if(current_user_can('edit_business_details'))
{
   // display your fields here.
}