Wordpress - Altering the appearance of custom taxonomy inputs

Sure thing, just use CSS and the 'admin_head' hook to make it disappear. I believe this is what you are looking for?

_{(source: mikeschinkel.com)}

Just add the following to your theme's functions.php file or to a .php file of a plugin that you might be writing. Note that I included an 'init' hook to define the "Home" post type and the "Bath" taxonomy so others can more easily follow the example. Also note that if your taxonomy is named Baths" you'll need to change the CSS selector to be #newbaths_parent instead of #newbath_parent:

add_action('admin_head','remove_bath_parents');
function remove_bath_parents() {
  global $pagenow;
  if (in_array($pagenow,array('post-new.php','post.php'))) { // Only for the post add & edit pages
    $css=<<<STYLE
<style>
<!--
#newbath_parent {
  display:none;
}
-->
</style>
STYLE;
    echo $css;
  }
}
add_action('init','add_homes_and_baths');
function add_homes_and_baths() {
  register_post_type('home',
    array(
      'label'           => 'Homes',
      'public'          => true,
      'rewrite'         => array('slug' => 'homes'),
      'hierarchical'    => false,
    )
  );
  register_taxonomy('bath', 'home', array(
    'hierarchical'    => true,
    'label'           => 'Baths',
    'rewrite'         => array('slug' => 'baths' ),
    )
  );
}

UPDATE

So it seems I missed the radio button part of the question. Unfortunately WordPress does not make this easy but you can make it happen by using PHP output buffering (via the ob_start() and ob_get_clean() functions.) Just find a hook before the metabox is output ('add_meta_boxes') and a hook after it is output ('dbx_post_sidebar') and then search the captured HTML for 'checkbox' and replace with 'radio', echo it to the screen and yer done! Code follows:

add_action('add_meta_boxes','mysite_add_meta_boxes',10,2);
function mysite_add_meta_boxes($post_type, $post) {
  ob_start();
}
add_action('dbx_post_sidebar','mysite_dbx_post_sidebar');
function mysite_dbx_post_sidebar() {
  $html = ob_get_clean();
  $html = str_replace('"checkbox"','"radio"',$html);
  echo $html;
}

And the evidence:

_{(source: mikeschinkel.com)}

or, if you're lazy can use this plugin: Single Value Taxonomy UI

(I would've rather added this as a comment to Mike's answer as it mostly does the same thing - but I can't yet add comments)