Chuck, if you have hunted elk before, you do can do a good DIY elk hunt in Wyoming. I have been on 4 such elk hunts in WY and have had good chances to fill my tags each time, finally getting it done this past September...
Several things:
1. Your 3 pref points should allow you to hunt a good unit, but not the best units. The current Eastmans bowhunting magazine has a feature on WY elk in the MSR section, which shows which unit you can draw with 3 points.
2. You can greatly increase your draw odds if you apply for the special tag, which is more expensive; in some units it will double your draw odds.
3. Try to get on a HMA; some are open to any elk tag holder and others require a drawing.
4. Join the Bowhunters of Wyoming; then your fellow members might help point you to the good spots (they did for me) and their quarterly magazine has good info on where to hunt.
5. Call the regional biologist once you narrow down your choices to a few units - some units are great for bowhunting but not for rifle, and for others the opposite is true. If you explain that you will only kill an elk with your bow, he or she may point you to a unit better for bowhunting.
6. If you apply for a late season rifle tag, the odds are even better to draw, and you can still bowhunt the entire month of september in almost all units.
7. If you fear grizzlies, you might avoid the units in western WY. Wolves will impact your elk hunting also. Might consider a unit with neither.