Its true, they will slow down a lot to keep their balance and run kind of like sideways. But even if you lose sight of one, keep running in that case. Some species tend to track you for miles, days in the woods. Some are not so bad, like black bears, but brown bears are horrible creatures. If you see a brown bear and you plan to camp that night, forget it. Its not worth the risk to have a brown bear barge into your tent at 2am like 10 miles away from when you saw it. They also have the habit of ambushing you. I know a lot of stories about bears and they do not end well. In my many encounters, I am glad it never ended up like in those cases.
Bad advice. You don't run from bears, that triggers their hunting instinct, and you can't outrun bears anyway (pollar bears are the slowest and they still reach 40km per hour).
What you do depends on the bear and the situation you encounter it.
NEVER get in between a momma bear and her cubs. If you do try walking away backwards while looking at the bear ( but don't stare into its eyes they might see it as a challenge) at a steady pace and don't make any threatening moves or alternatively play dead.
Generally you do one of three things:
You make yourself bigger and scream aggressively in case of black bear, you make yourself smaller, play dead and pray in case of brown bear, or you make peace with the fact that you are going to die in case of pollar bear( since they are pure carnivores).
Or even better carry bear spray and a gun , keep them handy and learn how to use them.