If you don't have a links.php for your theme, save a backup copy of your page.php (just in case), and then replace the following in the original page.php:
<?php the_content('Read more »'); ?>
with this:
<?php if (is_page('links')) { ?>
<?php the_content('Read more »'); ?>
<?php wp_list_bookmarks('show_images=0&between= - &show_description=1&category_before=&category_after=&title_before=<h3>&title_after=</h3>'); ?>
<?php } else { ?>
<?php the_content('Read more »'); ?>
<?php } ?>
For this to work, your bookmarks page has to be named Links with a page slug (permalink) of links. Change links in the above code to the actual page slug of your bookmarks page if it differs.