Okie dokie, here's my take on Ashe.

Movement speed (MS) is essential for her, seeing as she moves slower than most other champs. Putting MS on her will allow her to get away from incoming ganks a little better or chase down those pesky runners. Seeing as she has 2 slowing moves and a stun/slowAoE ult, it's very possible for her to get away from or chase down champs even when they have higher MS than her. To take full advantage of her potentially super high attack speed and slowing arrows, get MS.

2nd essential for her is critical strike (crit) and attack damage (AD). Most of her damage will be physical, and getting Infinity Edge helps to dish out a ton of damage.

3rd essential is attack speed (AS). To take full advantage of her slowing arrows and massive crit, AS is a must. Consider this: Your crits will have a 55% chance of occurring. Being able to put out 5 arrows in about 2.5 seconds = lots and lots of damage very quickly. The beauty of it is the champ you're hitting won't be able to run away as effectively, and if they try, you just use your ult, catch up to them, and finish 'em off.

4th essential is armor penetration (apen). Many players and intermediate bots like to build armor up, making it very difficult for Ashe to put out the insane damage she's capable of. Depending on how the game's going and how the enemy team is building up their armor, you can choose between Last Whisper or Runaan's Hurricane for the 4th item. If you can see that you aren't putting out as much damage as you'd like, go for Last Whisper and you should see improvement. If you're doing plenty of damage already, then go for Runaan's and tack some more damage on top of what you're already doing.

5th and last essential is life steal (LS). As stated before, most of her damage is physical, coming from her basic attacks, so why not get lots of health while you attack? Bloodthirster is pretty much icing on the cake, but it's mighty tasty. It's great for really clearing a heavily creeped out lane when mixed with Runaan's, since you'll be getting health from 3 creeps at once.

I know some players may gripe about her ult not being nearly as powerful as they'd like, and they want ability power (AP) instead. I like the ult, don't get me wrong, but I don't think it's the power of the shot that should get the attention.

Her ult is best used from across the map to support your teammates. An across the map shot with a 3.5 second stun and a small AoE slow around the hit makes this excellent for giving your team an edge that could very well lead your team to score an Ace. Even nicer thing about it is this ult doesn't have a very long cooldown (CD) compared to other ults. If you still don't think you could live without the extra powerful shot, I'd recommend switching out the Bloodthirster for Rabadan's Deathcap. Just remember, most of her damage is physical, so AP won't help you out nearly as much as additional AD and some LS.

Pros:

-Awesome across-the-map ult
-Super fast AS
-Lots and lots of damage (no need for Trinity)
-Slowing ranged attack
-Sheer creep obliteration
-Hawkshot = see incoming gankers before they ever get close
-Money maker

Cons:

-Extremely squishy until Bloodthirster is fully stacked, even then, be wary
-Not much MS
-No movement abilities, makes it hard to get away, ganks coming from the flank with stuns are extremely difficult to get out of, Flash is necessary, use Hawkshot to see 'em coming
-So squishy that even Barrier loses the point, Ignite for pretty much guaranteed chasedowns instead
-Long time to build, usually fully built late game