Go to Yellowstone National Park, in northwestern Wyoming. People have been coming here for well over a hundred years to look for, among other things, bears.
Understand that there are two kinds of bears, grizzly bears and black bears. They are not easy to tell apart, but there are more black bears than there are grizzlies, so you are more likely to see a black bear. That can be good, because the black bears are also usually less dangerous.
Understand that you have to work to see bears, these days. There is no shortage of them, but the National Park Service in Yellowstone will not allow people to feed them; it is illegal and dangerous. Because they are not fed, the bears usually have no reason to hang around people; they spend their time off in the woods somewhere.
Do not look for bears in busy areas, like around Old Faithful Geyser. This is the most popular destination in Yellowstone, but for some reason, bears do not think much of it. They appear in the area sometimes, but irregularly. Look instead in the northern part of Yellowstone, around Tower Junction and the Roosevelt Lodge. This is your best chance of seeing these elusive creatures.
Look also along the Northeast Entrance Road. Notice how the views in these areas are open; there are fewer trees to block your views. Since you can see more, you are more likely to be successful in spotting a bear. Finally, you can try along the big, open mountainsides north of Dunraven Pass, on the road from Canyon to Tower. Both black and grizzly bears may turn up here.