Yes, a bear's vitals are further back than you think.
The largest black bear I have ever seen - at least 400 lbs (spring) - I put an arrow tight behind the shoulder within 1/2" of where I wanted it to go. On a deer it would have been over in seconds - I never found that bear after a 3 hour track that ended in the rain. Another bear - quartering away shot from a tree stand @ 20 yds. Bears front legs were up on a log. Arrow entered behind the ribs and exited two ribs forward - skewered the heart.
An Alaskan guide had a video of where to shoot a black bear and his comment was "Half way back, half way down and 4" forward." Based on the bears I have harvested as well as those I have lost I believe his comment is right on (if hunting from a tree).
Also, in my experience, if you track a bear more than about 150 yds. you likely won't find him. Heart or lungs and they can be down and out in 30-40 yds. Liver and they will go 120-140 yds, lay up and be right there the next morning.
Good luck and as others have said, stay as calm as you can, remember your fundamentals and make a strong shot. I love bear hunting.