First, to directly answer your question: no, don't run. Running increases your heart rate, which increases how fast the venom will be spread through your body. It also increases the likelihood of another injury such as a twisted ankle, which would further delay treatment.
Your first priority is to distance yourself from the snake and any of its friends. Walk slowly (don't run) back the way you came. The reason you go back the way you came is because you can be more certain there aren't any snakes behind you, but there could be more snakes in front of you. If you can identify the snake before leaving, do so, but do not get any closer to the snake while trying to identify it. There's no need to capture or kill the snake.
The next thing you should do is find somewhere safe to sit down. Snake venom can cause loss of consciousness, and you don't want to be walking (let alone running) should that happen. Taking a break to sit down, clean out the wound, and come up with an evacuation plan will help ensure that you get to help faster than if you just start booking it for the trailhead.
To clean the wound, wash it out using clean (drinking-safe) water. If it's still bleeding, apply direct pressure until the bleeding stops.
My wilderness first aid book recommends then doing the following:
Apply lymphatic compression wrap with 6" ACE wrap, distal to proximal, then proximal to to distal; leave in place during evacuation. Monitor pulse and CSM.
In English, that means if you have an ACE wrap (like this) you should wrap it around the bitten extremity, starting further away from the center of the body (distal) and moving towards the center of the body (proximal), then back. The purpose is to apply a small amount of pressure to slightly slow flow through the lymph nodes as this is one way the venom can move through the body.
Checking CSMs means checking the circulation, sensation, and movement below the location of the bite. You want to ensure that the wrap doesn't cut off circulation, and should monitor whether the patient's ability to feel and move their fingers/toes is decreasing over time. You may need to remove and adjust the wrap if swelling occurs, this is why it's important to check CSMs every 10-15 minutes.
You can also optionally take antihistamines (like benadryl) to slow the body's reaction to the venom. This will not prevent tissue damage, but can prevent an anaphylaxic reaction.
Once the wound is cleaned and optionally wrapped, you can walk out, but walk slowly to avoid further injuries. Make sure to take frequent breaks to check if swelling has progressed and to monitor CSMs.
Some things to keep in mind about snake bites:
- Almost all healthy adults can survive a snake bite.
- Your recovery does depend on how quickly you get to a hospital.
- Therefore, don't take any actions that could delay your treatment, like running and thereby getting an immobilizing injury.
- Most snake bites are to the arms, hands, and face.
- Most snake bite victims are 18-25 yearold males.
- You might therefore conclude... that most snake bites are preventable.