Show Blogroll of another WordPress site

You have a couple of options here, but first let me advise you away from querying the database directly. If your sites are that closely related, then they should be in a Multisite network …

RSS

On Site B, fetch the RSS of Site A and display the posts and author attributions there. You can find any number of RSS plugins that do this for you or just get you started.

XML-RPC

Site B can also connect to Site A to fetch the latest posts using XML-RPC. You then have full access to data, including the most recent posts, as well as media, comments, etc.