You need to outsmart the bear, you can not outrun one.
One way to deal with a bear is to find his marking tree. That is a tall tree on which he reaches as high as he can and claws the bark. He will regularly vist this "marker tree" and see if any other bear has marked it. if his mark is still the highest, he will stay in the area. However, if another bear is able to reach higher he will leave the area rather than risk an encounter with a bigger bear.
Now, I used to have a woods camp in the backwoods of Maine and I got tired of finding the place trashed by a bear. So, I took a step ladder and a garden rake, found his marker tree, climbed as high as I dared and raked the hell out of his tree. No bears have been seen in that area since.
(Brains over bullets)