You are better off separating categories for posts and using custom taxonomy types for CPT categories.
You’d add this line to your register cpt code
'taxonomies' => array( 'bizdirectory-type' ),
Replacing this line in your code.
'taxonomies' => array( 'category' ),
And then add this code in your functions.php
add_action( 'init', 'wpsites_custom_taxonomy_types' );
function wpsites_custom_taxonomy_types() {
register_taxonomy( 'bizdirectory-type', 'bizdirectory',
array(
'labels' => array(
'name' => _x( 'Types', 'taxonomy general name', 'wpsites' ),
'add_new_item' => __( 'Add New Bizdirectory Type', 'wpsites' ),
'new_item_name' => __( 'New Bizdirectory Type', 'wpsites' ),
),
'exclude_from_search' => true,
'has_archive' => true,
'hierarchical' => true,
'rewrite' => array( 'slug' => 'bizdirectory-type', 'with_front' => false ),
'show_ui' => true,
'show_tagcloud' => false,
));
}