Unless you go to a state that has non-resident licenses like Colorado, your choises are few. Most elk licenses are done on a drawing basis. Here in Wyoming, non-residents apply in January.

Hunting with a bow is fine. Bow season in the Rockies is the absolute best time of the year. Fewer hunters, cooler temps, elk bugleing, aspen turning colors. . . nothing finer!

As far as tactics, it takes a lifetime to figure elk out. And still fool you. Old timers will tell you, "Elk are where you find them." (Smart asses.)
Cow and bull calling is popular. Even if it doesn't bring 'em in, it can at least help locate them. I like the "run and gun" method. I'll give a couple bugles, wait for a response, if I don't get one I move. (30 minute wait). Then do it again. When I get a response, then I move in. Using the cow call tocalm themandconceal my presense and maybe bring in big boy. All of this is on foot. And you need to be in good shape. Up & down mountains at 8 - 10,000 feet above sea level can not only take it toll on your body, feet and lungs, but it can make you physically sick. Called altitude sickness.
Best advice, don't come alone, watch every instructional video and read every book you can, practice for a year on your calls, hire a DIY outfitter, and plan on hunting next year.