bowhunting is closed to the public on public lands whenever there is a fire arms season in place (shotgun, handgun, BP/muzzle).
That's not entirely true... some public lands do not allow shotgun hunting, so you can bowhunt them during the gun seasons, but must wear the orange required by gun hunters.
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Tight lines & shoot straight.
Quit watching TV and go out hunting or fishing.
In Lake and Cook county, you can bow hunt during the whole season regardless if it's gun season or not. You aren't allowed to hunt with a gun in either county. So, that kinda answers part of your question