Ashe is a strong pick for a cheap price, she is an excellent farmer/harasser.

I run Flash/Exhaust to give myself both an offensive and defensive use. Pre 6 Ashe has no escape. Flash and Exhaust both allow her to escape the enemy. Offensively you can use Flash as a gap closer and Exhaust to catch up to your enemy. And it works nicely with your Frost Shot

I run a typical rune setup up

Greater Quintessence of Desolation
Greater Mark of Desolation
Greater Seal of Armor
Greater Glyph of Scaling Magic Resist

At level 18 this gives me

Armor Pen: 24.93
Armor: 12.69
Magic Resist: 24.3

I run 21/0/9

I grab maximize damage output in the offensive tree and ignore Havoc because it's easily countered with armor. Critical and Armor Pen is much more useful imho.

The Utility tree is specced for mana regen, allowing you to spam volley just a little bit more.

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I would go 21/9/0 grabbing extra armor and health but as a ranged character you should be hanging back grabbing as much farm as possible, not in the enemies face.

If Doran items aren't for you by all means skip them and go straight for the [[Blood Thirster] I try to get a decent boost in AD and Lifesteal with the Doran Blades netting me an easy 20 AD and 6% lifesteal.

The Giant's Belt makes Ashe less squishy and going into mid game she will need it as other champs start jumping on to her.

I build AS and Damage after this and get a Guardian Angel against AD teams Banshee's Viel against AP