Unless you are needing to purchase a bunch of gear, an out of state elk hunt is acutally pretty cheap. Your only cost would be the tag and some fuel. So, for example, Colorado tag is $670 and then I burn about $550-600 worth of fuel driving from NC and back. So $1200 for the hunt. Your drive would be much shorter, so less fuel.
Pack all your food, don't eat out at fast food places while on the road, don't buy a drink or snack at every gas station you stop at. Sleep in your truck or at campgrounds, no hotel rooms. It's really not that expensive.
Now, if you feel like you have to go out and buy a new pack, new bow, new set of clothes, new boots, new tent, etc. Then you are going to be spending a ton of money.