//swap out the category (33) for your own category
$links = wp_list_bookmarks('title_li=&categorize=0&sort_column=menu_order&show_name=1&echo=0&category=33&orderby=rand&limit=1');

//create array from string returned by wp_list_bookmarks
$bookmarks = explode('</li>', $links); 

//print without a link, if you want you could remove strip_tags() to bring the href back.
print '<p>' . strip_tags( $bookmarks[0] ) . '</p>';

http://wordpress.org/support/topic/adding-special-characters-between-bookmark-links-using-wp_list_bookmarks

Sometimes you just want a random link to display and outside of the default format, this works perfectly and removes all default html (list items / headings).

WordPress Links Manager - Display a random link from a category

wordpress, links

PHP