Thanks for all the responses guys, this is really helpful. Keep them coming!
Wudstix, you're not the first person who has brought up a hammock, and the idea is really intriguing to me. Is there a certain one that you prefer to use? I have a generic hammock (no clue what brand), but I have trouble getting comfortable in it since I'm a bit taller. What brand do you have?
Maclean, I was considering bringing both so that I can do just what you are describing. Set up the tent somewhere as our base camp and then carry the bivy in my day pack so that if needed we can spike out overnight. My only concern with the bivy and tarp is getting caught out in some nasty weather and waking up with water running under the tarp and soaking everything. I suppose picking a good piece of ground would be important.
Jim, that sounds like a good idea. Not sure my brain is fully developed either, so if I get in pinch, I might have to give that a try. OTC sheep tags would be a dream, I'm super jealous of that opportunity!
Clarkansas, I've looked at these floorless shelters and they look pretty nice! I like the idea of being able to set them up and have enough room to move around underneath. I still need to get hiking poles at this point, but they're on the short list.
So I've got a votes for tents, bivy's, floorless shelters, and hammocks. Thanks for helping me narrow this down guys!
I'll be in Idaho the first week of May bear hunting, but we plan on using the truck as base camp every day. I might bring a few options and see which one I like best, then go with that for the elk hunt. I'm looking forward to doing some testing, and appreciate the information on everything so far! Any other gear suggestions that you have learned about along the way on trips such as this would be really appreciated!