Bears can seldom run as far as deer, I think they have proportionately smaller lungs. That's why they tree when chased by dogs. The point being that a 150-200 pound bear isn't much harder to kill than a big buck. Bigger bears obviously are harder. IAE your firearm is more than up to the task.
If there is no snow your biggest issue is FINDING THE BEAR, fat can plug up holes and leave no blood. Look for kicked over twigs and stones (damp ground where they were lying) or broken off twigs- bears run like a locomotive through the woods snapping the underbrush. Ask your guide about it. I am pretty sure dogs are legal in Maine, if a tracking dog is available, Big Help. Have a cell phone, call the guide if you made a kill and have him bring the dog for tracking.
Don't fret too much, a lot of bears die about 20 yards from being shot. The last bear I shot turned and ran 20 yards. They sort of give a "death moan" listen for that.
If you are on a stand it is a good idea to make a mental picture of how high surrounding objects are and then compare that with any bear that shows up. Small bears have big ears, big bears have little stubby ears and sort of a "hog nose". Ask your guide about this as well.
Marshmallows. MASHMALLOWS??? Okay it seems really low grade but some bears come into a bait and then "hang up" in the underbrush. You can't get a clear shot. If you put some marshmallows about 3 feet apart on the likely trails going into the bait that often brings them in. Just don't ever tell anyone you did it.
PS: If you have skunk essence on your boots as a cover scent, don't walk directly to your tree stand. The guides tell this but most folks don't pay attention. A bear crossing your trail into the stand may pick up the essence and follow that and to the tree you are in and then start climbing the tree. If you are a bow hunter you cannot shoot straight down because the arrow can't stay on the rest. SO....walk over toward the bait FIRST so the bear goes there and then to the tree stand.
And...bears have a great sense of smell, I'd think about packing my clothes and boots in a leaf bag with some natural materials (pine needles) and have three changes of clothes and wash clothes after each hunt. Put your boots on at the hunt site, don't wear them in the vehicle.