The links are wrapped in a span:
<span class='editbio'>
<a href="/experts/3987/edit">Edit</a>
</span>
...
<span class='addbio'>
<a href="/experts/3987/edit">Edit</a>
</span>
How about something like
browser.span(:class, "editbio").link(:text, "Edit")
to get the first link vs
browser.span(:class, "addbio").link(:text, "Edit")
for the second link?
You can get a list of elements and tags you can use at Watir: Methods supported by Element.