You’d have to make a template page for your links, since sticking the code in through the editor isn’t possible, and add the code to that template file to call the bookmarks: <?php wp_list_bookmarks(); ?>
You should be able to include this tag twice, and have each show different categories using these parameters:
(string) Comma separated list of numeric Category IDs to be excluded from display. Defaults to (no categories excluded).
(string) The name of a Category whose bookmarks will be displayed. If none is specified, all Categories with bookmarks are shown. Defaults to (all Categories).
Then style the page into two columns. Or, run one tag in the page template, and one in the sidebar.