I think I have cracked this. Before 2.1 I used
<?php get_links('6', '<li>', '</li>', '', FALSE, 'name', FALSE, . Now the confusing part of it is that you thought by changing it to wp_list_bookmarks() that may solve the problem after the upgrade, that's wrong. The documentation needs polishing.
FALSE, -1, FALSE); ?>
This part in codex needs toughing up there is obvious syntax error there.
I failed the first time by using wp_list_bookmarks() because I assumed the category id is same as before, i.e. 6 in my case. It didn't work. What you need to do is to go to admin>blogroll and mouse over the category you want to display. You should see what id that is, i.e. ....link-manager.php?cat_id=xxx
I used the correct category id and that's working for me now, see sidebar of my site at which I have 3 links categories.