The BIO vocabulary can be used with RSS 2.0 if care is taken to avoid any specific RDF extensions. This essentially means that the date and place properties must contain only plain text. The most common use, however, will be the addition of the olb tag:

<rss version="2.0" xmlns:bio="http://purl.org/vocab/bio/0.1/">
  <channel>
    <title>Ian's Channel</title>
    <link>http://internetalchemy.org/</link>
    <description>Ian's weblog</description>
    <bio:olb>
      British; software developer; former CTO of Calaba; 
      author of OCS; co-author of RSS 1.0; developer of myRSS and Pepys.
    </bio:olb>
    <item>
      <title>Lack of Imagination</title>
      <description>Here's an RSS item</description>
    </item>
  </channel>
</rss>
    
    
    
    

It could also be useful to add the bio information at the item level:

<rss version="2.0" xmlns:bio="http://purl.org/vocab/bio/0.1/">
  <channel>
    <title>Ian's Channel</title>
    <link>http://internetalchemy.org/</link>
    <description>Ian's weblog</description>
    <item>
      <title>Lack of Imagination</title>
      <description>Here's an RSS item</description>
      <bio:olb>
        British; software developer; former CTO of Calaba; 
        author of OCS; co-author of RSS 1.0; developer of myRSS and Pepys.
      </bio:olb>
    </item>
  </channel>
</rss>