All bear Locations in BOTW
Solution 1:
There are two species of bear in BOTW, The Honeyvore Bear found in Tabantha Frontier and Akkala Highlands and the Grizzlemaw Bear found in Hebra Mountains and Gerudo Highlands. The bears spawn in the locations below (Light Blue is Grizzlemaw and Purple is Honeyvore):
You can check out the full interactive map here if you want to zoom in more detailed on the map, but this should be good enough to get you started. Just head to the locations on the map and change your Sheikah sensor to target the bear you are looking for.