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Why would you us a bow? Range is poor, and lethality is also low, esp. with the access the the ultra-wealthy have to medicine. When you hunt deer with a bow, you can usually expect to have to follow a blood trail, as it's rarely an instant drop.
Use a .300 Winchester magnum from 1000 yards; at that distance, you still have about 850 foot-pounds of energy, which is roughly double a 9mm at point black range. With the right ammo, that's more than enough to get the job done. You probably want a combined mechanical and ammunition accuracy of about .5 MOA range though, so that you have deviation of less than 6" at that range. It's a challenging shot, but it's definitely doable if you know your holds and can call the wind.
Bows can be roughly created from easily available materials, making it impossible to ban the ownership of.
Banning ownership becomes a game of catch. Use whatever you have: 7.62x51mm, arrows, rocks, ect.
And you can swap scopes depending on, uh, context.
You shouldn't need to. .300 Win mag is long action, so you're going to be using a bolt action rifle. There's not going to be too many contexts where you're going to want to swap out the scope for anything other than fairly long range.
Because it'll probably hurt more.