I haven't killed any deer with a bow yet. My only big game with a bow was a bear this year, while sitting. But this is public land in CA. I see more bears than bucks these days anyway.
That being said, I see and get very close to does all the time, though we can't usually shoot does. I think the closest I've come is about 10 yards on a bedded doe. I had a squirrel run up my leg last year while still hunting. This year, I had a squirrel blow by me about 6" away while stalking in on a deer I was hoping to find antlers on. Neither were aware of my presence. Sometimes, the more crunchy the leaf litter, the easier it gets. Yes, they can hear it. But if you go really slow, they often ignore it. Between the birds, the deer, the squirrels, the bears and every other critter out making noise, you just sound like woods noise if you're heading into the wind & take your time. 2-4 steps and wait a few minutes.
A few weeks ago, I took a nice buck with a muzzleloader. The deer were so nocturnal that I'd listen to them walk up on me in the dark (posted) and sneak off after they caught my scent downwind. One walked by camp while I was cooking dinner... Plenty came through in the middle of the night, too. But by shooting light, they were bedded up. It was a great lesson in hearing their footsteps, which I can try to mimic. As frustrating as it was, it was cool to have to focus solely on my ears to detect what's around me for hours at a time. My shot opportunity wasn't until I was hiking out and was beyond archery ranges. But the deer didn't much notice that I was there at all. It helped that the buck was pretty distracted by a doe...
Asbell had a great tip in one of his books -- use the ball of your foot to hit the ground first, then land the heel a split second after. Then the next foot the same way. Sounds like 4 legs instead of 2. I use it when I think deer might be within 50 yards or so. Seems to work. If I sound too much like a deer, they start looking for me and then the game is up. They're pretty darned social animals -- even our blacktails & mulies.