Meh, you can clear minions quick enough with just regular attacks.
Early game last hitting will net you the same amount as if you volley, because minions come at a fixed rate. Clearing minions too fast is just inviting a jungler to come and get you early game. Last hitting the minions while slowly drawing the opponent in so your junglar to get him is often times better.
You don't NEED flash in the situation I set up also. That is why I said Flash/Ghost, it depends on preference. Both can be used offensively as well as defensively. In bad situations such as your tank dying in a team fight it can be used to run away, ideally you never have to use it since Ashe basically has a perma-slow.
But against those Champs such as Kass or Ashe's or lizard-buffed champs. Having a flash to volley slow will save you more often than not. If you get snared or stunned... not much Movespeed OR flash can do for you.
If it is during late game, just poke the turret from range while your tanks/tank-dps zones them out.
Or if you have to backdoor, wait until your team baits them into a team fight. Then get the turret on your own. If they break off to come at you, just run back, they can't travel half the map in an instant, you just have to worry about the teleports. Map awareness is half the battle. If they are all MIA, you don't backdoor unless you have wards in that area, simple as that. No need to risk it even in a losing situation.
If you are already backdooring (by chance or them leaving the lane to chase the jungler), you can maximize you time attacking turret by timing how long is is since you last seen them on the mini-map and sending a hawk in the direction they are likely to come.
I never have issues with mana as Ashe unless I use my Ulti during the laning phase, the first 10~15 minutes, because volley doesn't do enough damage to be worth the mana cost in that time frame. Use the time in between last hitting to wait for crit chance to go up, that costs no mana and does even more damage.
Even as far as late game, I very rarely have mana issues even when harassing with Q toggled on. Volley is only used in my case to slow down an advance, hit a champ that is just barely out of range of my autoattack slow so my team can chase, or clear minion waves near a turret.
By the time I feel like I'm low, I've already went back to buy stuff like boots or my Zeal or even my BFS or have driven them off to heal or they have driven me off to heal.
Edit: Damn, wasted all that time and got Ninja'ed by ucal. Also added emphasis on the word "have".