I consider Ashe a great champion to pub, because she is versatile, can solo, go with anyone in the lane, do a lot of things early on and also carry the team to victory. She is also one of the most powerfull champions.
Always take Crystal arrow when you can no matter what
The first point should always go to volley. But there ends the standard skill build.
After that, If you solo mid and think the lane will be easy to avoid damage and you see this as a passive game, be quick to spend as much as you can on plentiful bounty. When you can't anymore, one point on frost shot and the rest on volley.
If you go mid and see a complicated lane go 1 frost shot and max volley, after that go plentiful bounty.
If you go with someone who seems to have a brain, max volley and frost shot. If it doesnt seem to have a brain and think you will have to play defensive go 1 frost shot and max volley.
If you go with someone and thing being agressive won't be profitable, and you will be able to farm with peace, max bounty.
The major challenge in pubs is when you don't have competent teammates, if that's true you can't rely on them too much.
I'm not a fan of teleport always. But i'm a fan of it when playing with unreliable partenrs.
Doing good teleports to take a tower, defend a tower or taking advantage of a huge amount of enemy creeps ready to be farmed, is crucial. Some people have teleport but I don't have a clue of why. Nothiing botheres me more than watchiing a 20 enemy creeps walking to my base ready to give the gold, and nobody doing a tp, or worse, a hero jungling near it like if 2 golems would be more profitable than 20 creeps. I've even seen hero walking near the 20 creeps like if 300 free gold and a bunch of exp isn't of interst to them.
For that reason I chose teleport when I pub.
The other spell can go from ghost/exhaust/flash.
I generally pick ghost because having only one combat spell that have too much cooldown doesn't sound very intersting to me(flash). Ghost can do what flash do most of the time, but has less cooldown. Exhaust would be fantastic if i can predict a JAX to be in the opponent team, but other than that,i find ghost more versatile. (also is great to do first blood, if you are sure you are going to lane with someone reliable)
So my standard is Teleport and Ghost.
If you go with someone reliable, go with Red elixir and nothing else. Even more if you have exhaust (even more if you have ghost and exhaust). With a good partner, the lane can be outrageous powerfull if you open with a red elixir. Still even if you don't have exhaust and go with my standard, open with a red elixir in a doble lane is fantastic imo.
If you go solo mid, i suggest open with boots and 2 health potions (or no potiosn at all actually if you go with teleport). Boots can make you a solid harrasser/farmer, and very hard to harrass. (taking one pot won't kill you).
Going with an early regrowth pendand is good too, for an early philo if you solo lane.
If you dual, you probably won't have too much gold. If you don't have that much gold, I suggest
If you solo, it depends on how well you are farming, going philo and 1 or 2 avarice is great if you are farming really well.
Philo is very nice always imo. After that it depends. If you are farming really well and seems like you will keep like that, i would do berzeker boots and a fast infinity edge.
Otherwise boots of swiftness, Black Cleaver, Zeal.
Eventually you will want to have Infinity edge, Phantom dancer, guardian angel
I can see good arguments against guardian angel, i just find it very good in pubs, since ganks are unorganized and team fights too chaotic. They generally get just close to kill you, but out of gas to do more damage toy you. I think is pretty cheap item for what it does in pubs.
Items you may need:
Anti tank green hand item(i don't remember the name): Good once you have a nice attack speed and there are a few too big champions to take down with more than 3000 hp.
Bloodthirster I don't like this item that much, but lategame when you just want more damage, i don't see better options a lot of times. But feel free to change it with green hand or black cleaver if you think it's better.
I think this is pretty straightforward, Red desolation, Yellow vitality , blue clarity and gold swiftness.
4 Veteran's scar
1 Presence of the master
1 Spatial accuracy
If for some reason you don't want to use the mastery trick, just go 21/0/9
If you go alone, go middle, is super easy to not get ganked or harrassed, especially with boots, farm until you get tired basically, farm, farm, farm , farm , farm.
If it gets complicated, use your superior speed with arrows + slow to get yourself out of danger, you should be untouchable unless against competent players, in whatver case it's strange to find in solo pubs.
If you go with someone in the lane, just pray for him to be competente, try to rush to the lane with him and gain position, use elixir and with critc, arrows and a few attacks, you should be able to take 60% of the life or more, if your partner have somethinig decent, is very easy to do first blood. If you really trust your partner, you can dominate the lane and allow your partner for free farm. Most of the time though you will be dissapointed he won't be able to farm properly and if he does, he will do nothing with his items. So generally is better to fight with him for the creeps and farm as much as possible.
Use teleport to push, defend, and go to farming sites. If the enemy push, be the last to arrive to the battle, maximize your farming time. In the battles, use your partners as cannon fodder, you just farm and kill people from outside the battle, take advantage of your extra speed and range. Never allow yourself to be exposed, use your teammates as cannon fooder.
That is, if you have any question, feel free to ask.