eBay would persue something with 'ebay' in the domain, they never mention about having 'Bay' as part of the trademark. I see r' Us as a unique entity, but Bay, is a single and common word. I guess you could have a problem if you directly compete with them and try to develop an auction site.
Here is what eBay says:
http://pages.ebay.com/help/tp/trademark.html