Screw kill count. Kills only look at your last hit on a champion. What matters is how much damage did you do overall, and did you stun them at the right time.

My Ryze has absolutely horrific kill count (maximum of 6 in a game where we ended with 40-10). My Karthus killed 7 people in my last game (final score 50-10), Rammus killed 22.
Overall damage--I lead Rammus by about 3 times. But he has 3.5 DoT ticks (2x Sunfire + Tremor, and he can taunt people onto his DBC), so he has a much better chance of landing the killing blow than me. But like I said before--I triple his total damage count, and quadrouple his assist (I was there for every one of his kills, but he usually isn't there when I tank for the rest of my team...as Karthus).

So screw kill count. If you do damage, and the opponents die to your team anyway, then it's good enough. Sure, it's important to be able to finish people off as DPS, but if there are other people who simply were "stealing" your kills (intentionally or not), then don't worry about it. But if you're the only DPS on your team..then it's a real problem.

Aside from ganks, Ashe should typically net less kills than other carries. Ashe's damage output is much lower than that of other carries for one main reason - she has no steroid. She has no AS boost, no AD boost. Kog has a damage/AS boost, Trist has an AS boost, MF has a damage/AS boost, Ezreal has an AS boost, Corki has armor reduce/true damage. Ashe has Volley and only Volley to buff her damage output, no AS or damage steroids. What she provides as a tradeoff is amazing utility in constant slows and one of the best, if not the single best initiation skill in the game. She's much more supportive of her team than other carries at the cost of mad deeps.

In my opinion get boots and health pots, stay in lane til bf- get infinity and two phantom dancers then win.

I use Flash/Ghost as summoner spells. Crystal Arrow + Flash to close the distance is almost as fancy as Crystal Arrow + Teleport, and far more efficient. And ghost... well it's ghost. Combined with Hawkshot and wards, ghost makes it almost impossible to gank Ashe in my limited experience. Exhaust would be a close 3rd choice, except that she already has a slow in Frost shot, so the only real benefit is the blind. But since you typically won't be trading shots with anyone, that's almost a non issue.

Thank you all for your feed back. I was mainly wondering if other people were using some sort of special build on Ashe to net her kills, but it seems they are not.

I've grown to learn how to get more kills and kill steals with Ashe instead of just assists. This is not a bad thing since you are a carry. The trick I've learned is to kill steal with a well-timed volley. Simple as that.

See, I used to have the same problem as this. Your build will do, it could be better but everything is situational. You may be squishy, but very early game, you need to harass and harass hard. Don't even harass, just kick their faces in. If you can get 2-3 kills early game, it's pretty much over because they will be scared of you. Most ashe's just sit back and try to kite. She's a carry for a reason, play her like one. If you really need survivability, I would go for a frozen mallet just for the extra slow if you're out of mana. I used to go about 3-5-15 or something like that, but now I end up going around 9-1-10 and carrying the team to victory.