There are a lot of variables when it comes to cost. Do you want to hunt during the rut (tons of excitement) or later in the year? Do you want a legitimate chance at a huge bull or will an opportunity at a representative bull suffice? Do you want to hunt in the aspens or do you want to hunt high desert?
Out of state tags and licenses can be expensive. Here is an example. For an in-state hunter in AZ a bull tag is $168 while an out-of-state hunter would pay $665; license is $57 vs. $160.
There are other costs that can quickly add up. I was very fortunate to get drawn to hunt bull elk during the rut in Arizona in one of the top elk areas in North America. The outfitter cost $5K (average price when I shopped around) which including a guide, food, and lodging. I then bought Swaro SLC 15x for glassing which added another $2K; my Vortex Viper HDs (8x) would not have sufficed if I had just brought them. I bought some additional hunting clothing, including better boots, which was another $1K. Meat processing was around $400. Taxidermy was $1K. I also used it as an excuse to buy a new rifle and scope which was another $1500 not counting a ton of ammo for practice. Since I live in AZ it only cost me two tanks of gas to transport the cape, rack, and processed meat; if I was out of state the cost would have increase significantly. I easily doubled the cost of the hunt on incidentals. Granted a serious chunk has been used for other hunts since then but it was still money that I had to pay. Now, I did get more than my money's worth from that experience. I learned a lot from the outfitter and guide (which has paid off on other hunts) as well as harvested a bull of a lifetime.
With all of that said, when I get interested in hunting a new animal I will go to Cabelas Outdoor Adventures to just get a ballpark idea of costs, what is usually included vs. excluded, etc. From there I will start doing more research and there are tons of web sites that will list individual big game by state and their cost to hunt along with contact information to various outfitters.
Here are a couple of things to consider. Take a look at doing a combination hunt. I've seen combinations including bull elk, mule deer, black bear, wolf, and mountain lion for not much more than the cost of just a bull elk hunt; overall score of the bull may be lower but you have more opportunities. You can also find deals on cancellation hunts. Find some web sites and check often since you'll never know what you will find. If this will be a one-time deal, consider renting high-end optics for glassing as you can save a buttload of money going this route.
I encourage you guys to do this. You'll have a blast.