In a normal fantasy novel when strange creatures like green octopuses or two- headed rats or giant were-bears are spotted somewhere, the first thing to do is to check: isn't there a secret genetic laboratory in the vicinity?
In fact there are
two of them close to Beorn's dwelling:
1. Radagast's Rhosgobel (that's why I like
The Might's theory) and
2. Dol Guldur, where a certain Necromancer is busy breeding all sorts of fell beasts, olog-hai, uruks, werewolves etc. Why not were-bears?
Perhaps some laboratory creatures had escaped and multiplied in freedom?