This build is something i worked on for fun. Before you judge keep in mind that i like to try things a little out of the ordinary, for anyone who thinks like me your welcome to give this a try yourselves. I have tried this out in practice games numerous times to tweak things i didn't like about it out.
Things to know before playing an ap Ashe:
1. You have given up the position of being called a carry, please do not fool yourself. Your new main task at hand is to support your team with your arrow of legend and your slows.
2.You must have truly mastered and played Ashe several times, your skill with ashes enchanted arrow must be second to none, you cannot afford to miss your shots all the time as you cannot rely much on your basic attack anymore for damage.
3.For the first 15 -25 minutes of the game your Ashe is basically just like any other Ashe and should be played as such. However, when later game comes around you must begin to play smart. You will most likely no longer be able to solo anyone in close range combat, so stick with your team for most combat situations and assist them by firing your Enchanted Arrow to pick off people that stray to far ahead of their group or save it for the strong dps on your opponents team (Like when twitch pops out of stealth to assault your team or when fiddle ults from the bushes.)After you use your ult you should assist your team members in chasing down enemies with your slow and volley. Your attacks will be much weaker than an attack damage Ashe but a slow is still a slow.
4.The Enchanted Arrow is a 1:1 ap ratio, meaning your total ap is what you add to the initial skill damage. For example, at level 3 Enchanted Arrow does 600 + (your total ap) magic damage.
5. Don't get high ap damage items first, to start it is more important that you have high cooldown reduction first. The ideal cd time you want to aim for is around 45 secs. The more times you can use your arrow the more useful you will be.
6.Let your team know ahead of time that you want to play support ap Ashe so they can properly arrange characters. Your team will automatically assume that you are a carry. If you do not say anything you might be lacking in damage. You don't want to set yourself up for failure in the character selection room.
7.Be prepared to be called a noob, there is a high chance that you will be insulted for choosing this type of build, as it is not something people expect of you. Don't even bother with this build if you cannot take criticism or you have fragile feelings.
8. Don't try ap Ashe til you have tried it many times in practice games. Using this type of build takes much more skill to use and is not as reliable as the usual type of Ashe.
9. Do not take mid solo unless there is absolutely noone else who wants to. You will basically doom your team this way, let your carries farm. Grab bot lane and focus on last hitting. the gold increase items you have will enable you to farm quickly.
Instead of just listing 2 summoner skills, i'll give options instead, as
I understand people have different playing styles. If you miss long range shots alot then clairvoyance might not be the skill for you.
Flash - really is needed to help with survival. Its almost certain that an opponent will reach you eventually if you are putting any effort into winning.
Clairvoyance- I use this to help my team scout and more importantly helps you keep track of your enemy team for use of your arrow. Clairvoyance has like a 40 sec cd with the mastery skill, so you will be able to use it a lot. You should watch the lanes for enemies that fall back behind towers, this means that they will likely teleport back to base when they have low hp. A few kills can be gained in this way with snipes. if you use this in place of flash or ghost i recommend care is taken. this is still a great support skill, but loses its value to me on Ashe as she already has hawkshot.
Ghost- As your basic attacks will not be as strong as a normal Ashe, it is important that you are able to flee dangerous situations. Also useful in the opposite sense, use this to help chase down/slow enemies believing they ever had a chance to flee. I use ghost/ flash as Ashe because she is slow, and you will most certainly be one of the slowest using this build with 370 ms. Escape spells will save your life.
I use armor penetration marks to help with early game. Although your attack damage is low you will still be auto attacking the same amount in order to slow. I don't care for magic penetration for the arrow as far as runes are concerned, remember that you are support now and your primary purpose of using your ult is not to do damage but to stun/slow.(It will still hurt a lot regardless)Your spell penetration boots and void staff later game should be all the magic penetration you need. I feel like its important to do well early game to get a good head start. If you find that magic penetration runes work for you then by all means that's fine too. This is just from my viewpoint.
That's about all i can think about for using ap Ashe. Let me say again that this type of build will never be better than an attack damage Ashe in terms of reliability. However i have to say learning to use this type of build was kinda fun. If you are someone who likes to try different things then this is certainly different. If anyone can think of another type of ap ashe build lemme know, I am always looking for ways to improve things like this.