Who would win a fight if black bear and Bengal tiger fought?

Depends on the experiences and age of each animal.

A bengal tiger would usually beat an asiatic black bear in a combat, but an american black bear would stand more of a chance. American black bears are bigger in size compared with asiatic black bears, and a very big male can come across a small female brown bear, in which siberian tigers prey on.

Asiatic black bears can weigh in size from 150 pounds to 440 pounds. American black bears are 200 pounds to 650 pounds. Bengal tigers weigh 450 pounds to 620 pounds.

Even though the american black bear and the bengal tiger lives in different continents, the weight and size of the american black bear over a bengal tiger would make the american black bear dominate over the bengal tiger.