For me, this was a fun card to build around. It's not the strongest weapon by any means and it has some significant drawbacks (exhausting and lack of damage), but it felt great when it worked. Let's break it down.
Pay attention to TRAITS, CLASS and more:
Spell: All the crazy stuff you're used to (already mentioned in other reviews and comments), like Robes of Endless Night or Prophetic. Don't forget cards like Prescient, Grounded (3) and Shining Trapezohedron. More on some interactions later.
Weapon: Bandolier and Prepared for the Worst both are interesting enablers, more the upgraded versions than the basic ones. Enchant Weapon was already mentioned in the comments.
Ranged: Use Snipe to make your one shot count or Marksmanship to shoot elite (!) enemies at connection locations with increased damage.
It's only level 2, so off-class Survivors or Mystics might play the Enchanted Bow, too. Being a double class card, it's at least okay in synergy decks. The existing Synergy cards are interesting supplements to the Bow (Join the Caravan for positioning or Gang Up for some proper damage). Especially mentioning Close the Circle, which does the same job as Wither (even better) by enabling mystics with another (fast) fight option for those odd health enemies.
It's a card, so it can be recurred with Resourceful. In my games, Enchanted Bow worked well with discard pile interactions like Resourceful, Short Supply, Prescient and the newly upgraded Uncage the Soul. So you could just discard it with Explosive Ward to deal 2 testless damage, if you're feel like don't needing the Bow anymore or want to recuring it later.
It costs 3, which might sound expensive but is the magic number for Uncage the Soul or Amina Zidane (or Rite of Sanctification + Robes.
EXHAUSTING (and SLOTS):
You have to ready the Bow (or bypass the exhausting itself) to attack several times in one turn. Therefore you don't have a ton of options, apart from "Ashcan" Pete. If you're able to put doom on the Bow (Marie's elder sign effect, being Amina Zidane or commiting Ghastly Possession, you could use the expensive permanent Sin-Eater to remove doom from the Bow and ready it this way.
Then there is the customizable The Raven Quill, which does several things for you. „Spectral Binding“ frees all of its three (!) slots, „Energy Sap“ puts more charges on it and „Supernatural Record“ finds it everywhere and plays it. „Interwoven Ink“ can solve the exhausting issue and ready the Bow, but only if Raven Quill is attached to another asset than Enchanted Bow (if I read this upgrade correctly).
Other ways to alter the frequency of attacks are (as mentioned in the comments) Akachi's Spirit-Speaker, True Magick or upgraded Sign Magick (but you have to solve the Slot issue, because you would need three hand slots in total). Another great idea is Knowledge is Power, which can work like True Magick (or additionally to True Magick's effect) or gives another shot with the played Bow while being exhausted. Upgraded Uncage the Soul is some wild idea: with it, after your first attack you could simultaneously discard and play it again from your discard pile, so it would be ready to shoot again for your third action.
Just 2 DAMAGE:
There aren't a lot of ways to increase the damage output, but here are my ideas:
Funny enough, (even if you're already using the sniping effect of the Bow), you may just play Marksmanship to get +1 damage (but it's a little expensive at 2 resources and 1 XP). I also thought of Hatchet Man (by evading first) or Bestow Resolve to allow commiting Vicious Blow (or Stunning Blow, simple to exhaust the foe). Bestow Resolve is especially nice, because investigators at connecting locations (where you as a „Sniper“ may sit) can also use this trick to help. Another option for big damage support in Multiplayer is combining the Bow with Gray's Anatomy. Michael Leigh also comes to mind.
Attaching Enchant Weapon (coming from yourself or an another investigator) for double „Enchanting“ fun is also nice while it gives +1 damage every round and boost your skill further during those important shooting tests.
If you're stuck with just 2 damage per turn, don't worry. For some enemies, that's already enough (especially aloof enemies, which tend do have 1 or 2 health). Of course, you'll need an idea how to handle 3-health enemies and bigger. Solutions could be fighting with events (that's what I did, with Parallel Agnes), spell assets (Brand of Cthugha is great for choosing how much more damage you need), fighting with your fist, being good with evading or using other tricks to kill (e. g. Garrote Wire) or exhaust (e. g. Pendant of the Queen, Stray Cat) the enemy.
ATTACKING, CHARGES and the fancy „SNIPING“ effect:
The true reason for anyone to play this card. Sniping (aloof) enemies from connection locations feels awesome! Aloof enemies aren't very common, but from time to time you'll see one (e. g. the Basic Weakness Accursed Follower with 2 matching health or in multiplayer Tony's Quarry. Then there are Acolytes or other hiding culstist at connection locations, which are very common and nice smaller targets to shoot.
Easy to miss: Targeting a (non-elite) enemy to ignore Aloof and Retaliate are only possible, if the enemy is at connection location! So with aloof enemies at your CURRENT location you have to engage them the old-fashioned way (or just move to a connection location). Good supplements for defeating enemies at connection locations are things like Dynamite Blast (for missing points of damage) or Grete Wagner (3) (for collecting Clues).
What about the charges? Obviously, you could refill them with stuff like Twila Katherine Price, Recharge or Winds of Power, but in my games (True Solo) this wasn't necessary. Remember, you may use the Bow with its normal attack (also against Elite enemies) even without spending charges. Of course, it's one more charge in total for Akachi, which might make the difference.
If you're only attacking once per round (which you probably do), make it count! Chaos bag manipulation will help (like Snipe, tricks like Live and Learn (don't worry about Retaliate!) or shenanigans like Time Warp and Recall the Future as well.
If you need to boost your skill, choose Daring (the Bow doesn't care about added Retaliate). You may attack with agility (nice for commiting Nimble and reposition yourself) or willpower, with +1 skill value. It can be nice to have this choice (like in multiplayer by managing the Making Preparations dilemma).
Evading, quick moving and repositioning yourself obviously are useful (or outright necessary to survive). There are a lot of options and helpful tools like Track Shoes (awesome card on its own and even better withe the Bow), Shortcut, Elusive, Mists of R'lyeh, Shroud of Shadows, Eon Chart, Archive of Conduits, Cat Burglar, Think on Your Feet, Bait and Switch... I also was close to finally play Lure (2) in combination with the Bow, but it didn't make the cut (same for the Predator or Prey dilemma, which could backfire).
By the way, one more nice supplement in my games was Power Word to use the non-elite enemies to collect clues, exhaust or damage themself and another, untill my Bow killed them after some turns.
All in all, I really like those semi-great cards and find was to make them interesting to play. Try the Bow!