The bow will make about as much noise.
Regarding the cartridge, while I generally prefer high velocity projectiles for whitetails without the silencer, when hunting suppressed I'm on board with subsonic, but IMO the best cartridge for that is big-bore (I personally use .44 magnum, bolt action like you suggest, 300 grain hollow-point at around 1050 fps). At that low velocity, you don't get much hydrostatic shockwave, so might as well make the biggest hole possible for an ethical kill. That lumbering freight train won't stop for anything, smashes right through bones. But even subsonic, it's a lot louder than a bow -- movie pew-pew just won't consistently put down something as big as a whitetail. Also note that at those low velocities, it's difficult to get bullets to consistently expand, so I do lots of terminal ballistics testing to find the optimal projectile and load.
For grandparent comment, too bad you have those hunting restrictions -- where I hunt, while this year's regs aren't out yet, for the last couple of years, anyone who wants to can shoot 12 deer per year (of which at most 2 can be bucks). They're trying to put a dent in the population, for various reasons including CWD, although I frankly think it's excessive.
[1]: https://www.silencershop.com/blog/post/suppressor-laws-by-st...
I seriously think a bow twang is louder
Somebody on the neighborhood listserv has advertised candle-light vigils for the deer at an adjoining field, but I haven't seen that in a few years.
If deer to human transmission is truly possible, then I would be worried about the possibilities here.
Not sure that this was meant and if that even makes sense.
Animals don't have medicine, so the sick or diseased amongst them can spread susceptibility to illness more readily, over time making groups more genetically or immunologically prone in a way that could lead to destabilization, become vectors for contamination (some cancers are contagious, like in dogs, and prions don't break down easily, making them true ecohazards), or end up as vectors as they contact other animal populations (HIV and swine flu were non-human origin).
Predators also encourage migration of herds, so deer won't consume an environment to depletion, including crops.
Predation is nature's free labor!