Hmm. I may have spoken too soon. I think the cedar does need to be avoided after all. I just checked the HRS website, and here is a link to their article on cedar, though it's in litter use.
http://www.rabbit.org/care/shavings.html I copied a paragraph that answers your question:
"When you open a container of pine or cedar shavings you will instantly smell the "aromatic" nature of the litter. That smell is where the the problem lies. The odor is from the natural volatile chemicals in the wood called phenols. Thus one of your best detection methods for determining an unknown bag of shavings is your own nose! This odor, and the phenols that cause it, are not found to the same amount in hardwood shavings, thus hardwood shavings, aspen being one of the most common, are considered a much safer litter material and can be recommended for rabbits and other small animals."
So my suggestion now would be to be on the safe side and return the bed in exchange for one without cedar. I expect that would be very easy to find, and it still is a good idea as a training pillow for your couch problem. But why worry unnecessarily when a safer cushion can be had?