Having handled snakes most of my life and being around them (including cottonmouths) the last thing you want to do is elevate the limb right away.
Here's why:
Elevating the limb will only accelerate the transfer of the hemotoxic venom between the bite area and the heart if done right away.
In this instance, wait.
First apply a constricting band (not a tourniquet) a couple of inches up above and below the bite area, and if possible, disinfect the bite area with an antiseptic
If you have a kit and are not squeamish, if you know what your doing, make incisions with the blade across the bite area.
Remember that the venom sacks are located at the top of the snakes mouth. Don't worry about any opposing marks.
Use the suction bulbs to try and evacuate what you can of the venom. This has to be done quickly to offset as much hemotoxic damage as possible.
In the absence of a kit, as long as you or another person has no open sores in their mouth, you can suck it out that way. And no, you won't die if you wind up ingesting some of it (myth)
Get a cold compress on it as soon as possible to help "slow the flow" and keep the swelling reduced.
Check the constricting bands from time to time as the swelling will increase and the will eventually become tourniquets if you don't.
Also, get any bracelets, rings, watches etc off of the victim immediately (especially if it's a Rolex
) before the swelling takes effect (and it will very rapidly)
Then, keep the affected limb even or slightly elevated, monitor for shock, continue to check for swelling and transport immediately.
I was there when a buddy of mine (and fellow handler) was bit by "meathooks" an apppropriately named moccasin (because of his size and girth) who wasn't cooled down (refrigerated) long enough prior to handling him.
After he got him out and applied the hand hold technique, he began to writhe himself loose.
When the handler began to realize meathooks was seconds away from muscling himself loose, he attempted to drop him back in the box. He then extended himself and made an explosive launch and subsequent bite to his arm.
Everything I just explained was applied in this incident. This can be applied to almost all venomous snakes, including copperheads, which, unlike moccasins, are not aggressive.
Now for the irony: He was medevaced to an AF hospital ER. When he got there, the ER personnel mistook the constricting bands for tourniquets, who then loosened and opened them up.
He flatlined almost immediately and almost lost his life. He was successfully resuscitated, but had a lengthy recovery and suffered large amounts of skin loss and tissue damage.