I think it depends. Unicorns are quicker than bears. And they often are depicted as having wings. If the unicorn has wings, if it can't fly, it will probably be able to glide a bit, or at least run faster. Not to mention those horns can be really sharp. The bear has a lot of brute strength, sharp claws and teeth, and a very heavy body. It's also of course not as fast as a unicorn. Naturally this would usually equate to a an aggro-midrange versus an aggro-control style battle of sorts, with the unicorn using its magic combined with hit and run tactics to tire the bear, and the bear trying to land the one or two hits it needs to kill the unicorn before the unicorn can get out of its range. Of course, if the unicorn gets really angry, it might try a charge with its horn. Against the bear this tactic probably has a relatively low chance of success in spite of the bear's low reflexes. If the unicorn gets angry it will likely make loud hoofsteps and possibly neigh, giving the bear more than enough time to react to the charge.
And this is all without the supervision of a mage.
So in conclusion, it could go either way, but the unicorn has the advantage.