As mentioned, unless you have serious coin to throw down for a private management elk, you'll likely die waiting to get drawn. With that said, I have a friend up here that actually drew a Bull Elk tag from the La Panza herd here in SLO County. He was able to score on public land, too, which is very unusual. The crazy thing was his wife drew the tag the very next year. It was crazy luck. She got hers on public land near the Carrizo Plain from days on horseback. What usually happens is these herds get wrapped up on private land during the season and even though you have a tag, the landowners will charge you at least $5k in trespass fees. I know several guys that have got their Elk Grand Slam and had to pay $15-20k to get that last one they needed, the Tule Elk we have here.
Depending on which unit, you can usually always score a Cow Elk tag in CO. Just pay the $$.