I can't offer any advice on hunting public land, unless it is huge like some of the wilderness areas out west or the Everglades, then I would say "find the thick stuff, and don't move around unless necessary"
I hunt a private timber company lease, and I have bowhunted during gun season. It is tough as down here running deer hounds is legal. I go out late morning, and hunt through lunch when a lot of hunters return to camp for lunch. I've seen deer and hogs "sneaking" back to their bedding areas after being spooked by dogs, atv's and hunters.
Hunting early morning or late evening is futile here, the deer go nocturnal pretty quick. I have never taken a shot with a bow during gun season, but I have seen game.
If I do carry a bow, I also carry a .41 or .44 revolver in case I can get a shot out of bow range,........or I just grab a rifle and join the crowd!
John