Child Theme

A child theme should be possible. Do it all the time.

You should create a folder containing at least a css file and a screenshot and upload it to folder wp-content > themes

The css file should contain at least this:

/*
 Theme Name:     GridBullettin Child
 Description:    GridBullettin Child Theme
 Author:         Guido van der Leest
 Template:       gridbullettin
*/

/* Imports styles from the parent theme */
@import url('../gridbullettin/style.css');

Note: a better way to import styles from parent theme is to create a funcions file in your child theme with this:

<?php
function enqueue_child_styles() {
    wp_enqueue_style( 'parent-style', get_template_directory_uri() . '/style.css' );
}
add_action( 'wp_enqueue_scripts', 'enqueue_child_styles' );
?>

Guido