The hook user_register should run just the same as when you’re registering a user not through AJAX..
https://codex.wordpress.org/Function_Reference/wp_insert_user#Notes
However the function wp_insert_user will return the new user id if successful so you should be able to do this right after:
update_user_meta($user_register, 'number_of_bedrooms', $_POST['fields']['field_55e56dfdabccb']);