Much as I like to shoot from prone, I don't find it very useful in the field. Now and again I can take a shot from prone, but often it's just too low given grass, brush and other obstructions that get in the way. Mostly, I've shot game from sitting. I practice it regularly, and am able to shoot very accurately from sitting. Standing... Normally I use it only for close range, but this year I branched out and took a mule deer doe at 400 yards from standing... Of course there was this wonderful dead tree to use for a rest! My buddy took this photo right after I'd shot the doe, while I was watching to see if she needed another shot. She didn't.
If I hadn't had that tree with the perfectly placed branch... I wouldn't have even tried it from standing. As it was the bullet went into her chest, pretty well trashing the heart and lungs and resulted in an instant kill. Note the sling on the rifle... My favorite aid to accuracy:
Mostly though I use sitting, and although I've used the bipod, I'm one of those sling nuts... Too much NRA Highpower shooting perhaps? For whatever reason, I've always enjoyed shooting with a sling for stability. Earlier this year I took a young mule deer buck from 175 yards, from sitting, with the rifle sling rigged as a loop on my upper arm, just like on the firing range. Put the bullet right through the buck's shoulder blade, exactly as intended.
My son often uses a tall Harris bipod to help him stabilize the rifle, particularly while sitting:
This year though, he took his mule deer doe from kneeling, a position my knees no longer tolerate:
If I can get a rest, I'll use it. The bipod is handy, but I don't like them all that much. They seem to destroy the balance of the rifle for me. I'll use them from time to time, but they're not my favorite tool. Often I'll find some way to rest the rifle on my hunting pack. That works out real well for me. If I can't get a rest, I'll do what I can with the rifle sling - and that usually works out real well for me. I'd love to take more field shots from prone, but it just seems like quite often prone simply won't work. I do a lot of shooting at the range from standing and sitting. The groups aren't nearly as good as from prone or off the bench, but it pays off during the season.
You asked specifically about elk. I used sitting, with the same loop sling to take this bull:
Sitting was the only real answer. Prone wouldn't clear the grass & low branches. Standing wasn't a good idea considering the small "window" in the branches I had to shoot through. Sitting worked perfectly, and I used the sling to stabilize the rifle.