The .270 will work fine for bear, just use the heaviest, most durable bullets that you can find. The Nosler Partition is an outstanding bullet for hunting larger animals such as black bear. Black bears aren't bullet proof by any means, but they are much tougher than deer. Make a good shot into the heart/lungs of one and he won't go far. Don't try to get creative and shoot for the head, you are more likely to miss or wound the bear than to kill it.
The most terrifying sound in nature is not the roar of a charging lion, nor the whistle of a descending bomb; rather it is a click when you expect a bang.