It looks like you were in the visual editor and so the shortcode is not being interpreted. You should enter these, and all shortcodes, using the text mode editor.
When you are editing the page just click the text tab on the top right of the edit window and then type the shortcode.
Looking at the source it shows this:
<p>[<span class=”GINGER_SOFATWARE_correct”>social</span>-bio id=308]</p>
instead of [social-bio id=308]
This is because the formatting that the visual editor adds.
Also, you need to make sure that Shortcode [social-bio] under When to Display Social Author Bio is checked in the general settings for the plugin.
Let me know if this works for you.
Nick