Ashe is an initiation champion, not a kite based champion like Ezreal is. Your job is to go on the champion when they have no alternative means of escape other than flash or using their mobility in their kit. She has a slow for a reason, which allows her to get her 4 autos in + attack speed to assist. A good Ashe isn't just gonna willy-nilly dual anyone without having her support or Ult up. Not only that, she's an ADC. She is suppose to be farming, not just roaming around with no CS. Because autos stack also off minions, you nearly ALWAYS should be able to have your Q unless you insta-clear a wave with your e... which is bad farming technique and most likely will have your lane pushed more often than not (which allows the enemy jung to gank several times).
If you learn to freeze lane and maintain her q, not just shooting ult across map HOPING to ks someone, then you are going to do fine. Otherwise, you're gonna over push your lane, get camped all game (cause' Ashe has 0 mobility) and otherwise lose lane.