Most likely, you would want to hook into the $post query and grab that information right then by doing a JOIN to your table.
hook location - showthread_query:
PHP Code:
$hook_query_fields .= ",yourtable.field as field";
$hook_query_joins .= "LEFT JOIN " . TABLE_PREFIX . "yourtable ON(whatever)";
And then in the postbit_display_start hook, something like:
PHP Code:
$template_hook[postbit_start] .= 'This field:' .$post[field];
Something like that. Play with it cuz I haven't tested it (obviously, since I don't have your tables).