A bite usually occurs to the head or face in a dog. The swelling is immediate.
Oftentimes the bite location is not visible, and there is no real test that I know of. But the swelling is so severe that a person usually figures its a snake.
The swelling can be bad enough that the eyes shut, and the skin can sometimes tear. They drool a lot, but if you catch it early enough the dog is not in a great deal of apparent pain.
I guess the idea is that if your dog's head is twice the normal size and its warm enough for the snakes to be out, they get the anti venom.
Luckily, a dog that is not snake bit will not be killed by a dose if you have guessed wrong. You are only out the 600 bucks!