Recommendation used to be to use a constricting band (that’s not a tourniquet) and seek medical attention.
I learned that years ago too - looks like that’s no longer recommended. Though in the case of bites from neurotoxic elapid snakes:
“non-spitting cobras, mambas, kraits, coral snakes, sea snakes, and everything in Australia”
a pressure-immobilization bandage applied with the modest tension you would use to support a sprained ankle is proper protocol now.
But most if not all of the neurotoxic elapids are not native to North America.
The protocol specifically states, however, that bites from vipers (rattlesnakes, water moccasins, and copperheads) should NOT be treated with a pressure-immobilization bandage.