How to Make a Bow-Kata Monk/Fighter?

[SociopathFriend]

Not really an optimization thread so much as one curious about a concept and how to best go about building it.

You see with movies like Equilibrium and now the FF7:Remake- I'm quite fond of what is commonly referred to as "Gun Kata" AKA "martial arts with guns".
Now in D&D I'm curious about making what I would call "Bow Kata" or obviously martial arts with a bow.

The idea is that our only weapon is the Longbow- whether at range or in melee. With an emphasis on skilled shooting that goes beyond the standard what most people can do and wielding the bow in melee to a potential few can match.

To my way of thinking (no Unearthed Arcana and Point-Buy being the prime points) the best way to go about this would be Kensei Monk and Battlemaster Fighter.

Is this the way to go about it? If not what would you suggest? If so then what all should I be looking for to better build on it? Sharpshooter for example seems a given.

Note:
Kensei Monk may pick one melee and one ranged simple or martial weapon to be their Kensei Weapon- which then functions as a Monk Weapon.
My understanding is that the specifics of Monk/Kensei Weapons trump the general rule of Ammunition weapons being Improvised Weapons when used in melee but even if it didn't you could simply state you kick someone or punch them in melee and you'd have the same exact damage so arguing about that particular part seems a waste of time.

Note again:
I understand Crossbows are a thing- I don't want to use Crossbows or Hand Crossbows.