It is tough hunting, but you can easily find areas to get away from others during bow season. It won't quite compare to private land, but there is a lot of it (Truman has something like 110,000 acres of Corps land)and there are plenty of deer. Missouri is generous with their firearms seasons and they have alternative weapons season, doe season, etc. The rifle season is crazy on much of corps land.
You can find nice deer on the public land though. I had a 180" deer bed 60 yards from me last year... for 5 1/2 hours!!! Thought I was going to die! :-) I really enjoyed watching the ol' boy. Killed a decent 10 pointer on public last season.
Look me up if you get by this way.