There are many, many bears in Alaska. If you keep your eyes open you are likely to see them along almost any road, in the area of Exit Glacier, Portage Glacier area and sometimes even in Anchorage....in the city.
There is a running (decades long) joke in our family that if you want to see a bear, follow me! My family has a house out in the area east and south of Anchorage not far from Turnagain Arm. During the warmer months, there are bears just about anywhere I want to go.
If you see a bunch of cars/trucks pulled over along a road, chances are the people are seeing animals. Most tourists drive to fast and miss so much.
It goes without saying, leave the bears alone! You don't have to pay to see bears, just keep a look out. The same with moose.
Be sure to take a pair of binoculars as you will use them plenty.
I wouldn't take the time and effort to drive to Fairbanks. You have plenty enough driving to and fro Denali Park. That road can get very congested and slow. Don't set yourself such a tight schedule that you turn your vacation into a JOB!