Hello,

i checked your current website but the sitemaps are ok, so it's not a problem related to the sitemap component itself.
Rather it looks a problem of redirections and because Bing it's not so smart as Google it may have issue.
I think that you have installed sh404sef and that could a problem for Bing when accessing the website.

I recommend to try it again AFTER your migration to Joomla 3.6 with all extensions updated.
However you can try a few things:

1. Configure sh404sef properly for JSitemap as reported in the PDF docs attached
2. Submit raw sitemap links such as: http://www.guillenphoto.com/cms/index.php?option=com_jmap&view=sitemap&format=xml&xslt=1&lang=en and http://www.guillenphoto.com/cms/index.php?option=com_jmap&view=sitemap&format=xml&xslt=1&lang=fr
3. Ensure that the Bing Bot is not blocked by other plugins or server (contact the hosting provider)
4. Disable the page cache plugin. As of now i see it active and XML headers are lost in such case. Not sure if that could be a problem for Bing.
5. Ensure that sh404sef has not anti-flood or other security features enabled

Hope this helps.
Regards