Bears do not eat fish.
You just toss the food item such that it lands close to the animal. If it's an item the animal likes, it should usually eat it. It seems like sometimes the animal won't eat for whatever reason, but if you leave the area and come back they should. You can only feed them once per day.
I got this list from
here. I haven't checked all of them but I bolded the ones I can confirm.
Bear:
Honey, turnip, potato, tomato, sweet potato, bok choy, carrot, strawberry, corn
Panda:
Bamboo grass, turnip, potato, strawberry, tomato, carrot, sweet potato, bok choy, banana, grape
Fox:
Egg,
black egg, potato, strawberry, tomato, carrot, sweet potato, bok choy, fried tofu
Tanuki:
Egg,
black egg, tomato, bok choy
Rabbit:
Carrot, corn,
turnip, sweet potato
Weasel:
Egg,
black egg
Monkey:
Egg,
black egg, sweet potato
Pig:
Egg,
black egg, turnip, tomato
Chickadee: Wheat,
corn, rice
Mouse: Corn, cheese
Duck:
Medaka-type fish (any size),
Wakasagi-type fish (any size)
