I'm going to assume you're in low ELO.
It's highly frustrating, but yes, the first rule of trying to main ADC is that you need to realize bottom is going to be a 1v2 every game, EVEN if your support is there, because pretty much no one is good at support in low ELO. And even though that means the enemy support is bad, that doesn't change anything because all it takes is one simple mistake and you can be in a position where bot lane is now unwinnable even if you are technically a better player than your enemies. Just because you're a better player doesn't guarantee you win the lane - sometimes the winner of the laning phase is decided during champion select, at which point you just have to passively farm the first 10-15 minutes of the game and then hope you can carry mid to late game.
The good news is as long as you don't die, losing the bot turret isn't the end of the world. As long as you survived, and you can CS under turret, it's fine. What's bad is when you give up turret AND die multiple times. This is why most people suck at the game, because they don't understand that there's a right and wrong way to lose lane. The right way to lose lane is to survive and get whatever CS you can, the bad way to lose lane is to lose turret AND die 3 times AND start bitching at your jungler AND sitting in base waiting for the 20 minute mark to roll around so you can surrender. You were playing Ashe, so technically you should've been rather difficult to dive. You have 2 slows, an E that lets you scout incoming ganks, and an ult that can stun the people diving you. Even if you were dying, you should've been taking one person down with you.
I do not recommend leaving lane. This is because with your support gone, you're actually getting bonus experience, and since Ashe is a team-fight oriented champion, you definitely want to do everything in your power to get those levels so you can do well going into mid and late game. If you run mid to join Malphite, you can't really do much because even though Ashe has a strong ultimate, her spike is not as effective as Malphites. All Malphite has to do is press R and soak up damage, so he's good to go at level 6. You on the other hand need items because you're the ranged DPS, so if you run mid at like, 8 minutes into the game after you had a crappy laning phase, you're not going to be much of an asset to your team once you get there. You won't be putting out the DPS you need to, you'll die the moment you get caught by some enemy CC, and because the enemy bot lane is ahead, once they come mid you'll lose the team fight regardless. The best option is to stay bottom and just keep farming until you know you have the items required to make a difference. On Ashe, I usually do not stop farming until I have Greaves, IE and Shiv/PD. Once you have those three, you're ready to group. I see a lot of ADCs make the mistake of buying like, pickaxe and Greaves, and then running mid thinking they're going to be a threat. No, you're just going to get deleted in 1.5 seconds by the enemy LeBlanc.
If you find it increasingly difficult to win with Ashe, play ADCs who are hard to lock down. Tristana and Blue Ezreal are good examples of this. Similarly, if you suck on Ashe, you'll probably suck on all the immobile ADCs, like Varus and Kog'Maw, so don't pick them.