Your options are somewhat limited because most of those listed are drawing only. Colorado and Idaho areprobably the only good options for over the counter type licenses. And you have to be careful about some areas in Idaho due to wolves lowering the elk population. That proably leaves Colorado as you best option.

How much time can you take off school to hunt. A basic elk hunt would involve getting to the area a day or two before the season opens, the hunt would take a minimum of 4 to 5 days, then the trip back (minimum of a week total). Then you have to figure time to get an elk out of the woods. How were you planning to get a big animal from 3 to 4 miles off road to your truck (on your back on with horses)?

As far as a specific place in Colorado, the Colorado division of wildlife is a good place to start. Most areas for bowhuting are OTC. Another good choice would be the first rifle season, but you have to put in and draw that tag. However, many areas can be drawn with no points, just have to do some research. If not, the 2nd and 3rd seasons are mostly OTC.

Good luck