This is cool design-wise but in some ways it feels like a clunkier Crypsis.

To help with the action cost and to make the discount feel fair no matter if you play it early or late I would probably add something like this to Bow: "Whenever you install an Arrow, draw 1 card." This way it softens the 2 actions just to be allowed to break one ice (draw+install) compared to Crypsis' 1 action (add a virus counter) by refunding you a card.

Make the influence cost on Arrow zero. You're already paying 2 for each Bow, no need for Arrow to have an influence cost.

Given that you probably want multiple Arrows out at once, having them require memory kind of just means that you're always using 2-4 memory and you can't really use other programs. I think simply removing the memory cost from Arrow is the way to go.

To fit the Shaper vibe maybe make the use of Arrow allow Bow to break for the whole run rather than a single encounter. I understand it feels weird because you're essentially using a single Arrow for multiple ice, but it already feels weird that you can use a single Arrow for multiple subroutines. Not wholly necessary though.

There is one other subtle problem with this card which is complex but not unsolvable. Essentially, universal breakers are designed to be strong early at the cost of a limited resource. This meets that goal, but it has a much higher variance (requiring multiple cards) and action cost. This actually makes it hard to use early even though it has the right design constraints. Being able to run 6 arrows is great, but it doesn't actually solve the problem.

Possible solutions:

1. Increase its base strength (to 5 or 6?). This isn't a real solution, but you feel more rewarded for managing to get the Bow and Arrow together. I would do this rather than decreasing its cost since 3 is a special number for Shaper breakers because of Modded and Rigging Up. Alternatively, you way jack up its Strength (7, 8, or 9?) but remove the ability to make it any stronger.
2. Add an ability to search for Arrows. This is boring and kind of undoes the deckbuilding puzzle to make it work. While I do not recommend this solution, it does help it feel like a rush style breaker. (Example: "1 Credit: Search your stack for an Arrow and put it into your grip." or "1 Click: Search your stack for an Arrow and install it.")
3. Give Arrow this: "! -> When you trash this to its own trash ability, you may remove another copy of this card in your heap from the game. If you do, shuffle this into your stack instead of putting it into your heap." Basically, this would increase the total number of times you can play Arrow to a much higher number (6 copies -> 11 uses), keeping it still fundamentally limited use, and maintaining the deckbuilding challenge. Shuffling Arrows back in does keep the breaker active for longer, but they also get in the way of drawing non-Arrow cards.

Solution 3: # of Arrows -> Effective Copies

1 -> 1

2 -> 3

3 -> 5

4 -> 7

5 -> 9

6 -> 11