Using image caption from media library?

I’m not familiar with the WP Biographia plugin, but these are the ways available to add a caption if you can modify the structure of the biography display.

You can add captions via the shortcode like this, if you want them to have the same layout as captioned images in your posts:

[avatar user="admin" size="medium" align="left" link="file"]Photo Credit: Your Name[/avatar]

In order to make this code dynamic, you’d have to put it directly in a template like this:

<?php echo do_shortcode('[avatar user="'.$user_id.'" size="medium" align="left" link="file"]'.$caption.'[/avatar]'); ?>

In order to get the caption that you’ve stored in your database, you would have to get the post_excerpt value of the attachment ID, which is stored in the usermeta table. You can get the value like this, if you pass the correct user ID which I’m assuming is the post author:

global $wpdb, $blog_id, $post;
$user_id = $post->post_author;
$wpua = get_user_meta($user_id, $wpdb->get_blog_prefix($blog_id).'user_avatar', true);
$caption = get_post_field('post_excerpt', $wpua);