No, at the moment, it is not possible to get armour for you bear.
The Compendium search page can be used to find all items which can be used in a companion slot by selecting "items" in the Search: list box and "companion" in the Category: list box, before selecting Apply.
At the moment, this lists half a dozen items from Adventurers Vault, none of which are armours. As wax eagle's answer suggests, the closest thing to armour would be Companion's Defender, which provides a scaling bonus to all defences.
After seeing the comments here, I asked the What options are available for a Sentinel Druids Animal Companions item slot? which I was able to answer myself after hearing wax eagles answer.