The TL;DR reply is that at the moment you can't do this. WP Biographia allows you to automagically add the Biography Box to all types of archive page or not at all. The ability to break out which sort of archive page, tag, author, category, etc, will probably be in a future release of the plugin, once I a) work out how to do it reliably and b) have the time to actually do it, test it and release it.
The longer, and hopefully more helpful reply, is that this is a known shortcoming in WP Biographia. My post Bending WP Biographia To Your Will, sums it up like this ...
Display Gotcha: If you choose to display the Biography Box on post archives, this will do so for all archive types, be that tag archives, author archives, category archives, date archives or so on. If you want to restrict the display to a particular type of archive, you’ll need to add some conditional tags to your theme’s template files.
... this is because WP Biographia currently allows you to automagically add the Biography Box to the front page, individual posts, archive pages, individual pages and RSS feeds by using the corresponding WordPress API functions to work out what sort of page is being asked for (
Filtering out the differing types of archive page needs some more conditional code to be added (
is_category for category archive pages,
is_tag for tag archive pages and so on) plus making corresponding settings and options for this. All of which is doable, but needs to be written and tested.
There is a work around to what you're trying to do but it's far from elegant and requires some not insignificant theme template hacking. What you'd need to do is stop WP Biographia for automagically appending the Biography Box to archive pages and then, for each type of archive you want to have the Biography Box displayed on, category archives in your case, ensure that your theme has a category archive template, locate the code where the WordPress Loop is being processed and use the
[wp_biographia] short code to insert the Biography Box. How this is done precisely will vary from theme to theme.
Hope this helps